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book.bib
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@manual{sage,
Key = {Sage},
Author = {Sage},
Title = {{F}ree {O}pen {S}ource {M}athematical {S}oftware ({V}ersion 3.0.4)},
note= {{\tt http://www.sagemath.org}},
Year = 2008}
@book {shoup:book,
AUTHOR = {Shoup, V.},
TITLE = {A {C}omputational {I}ntroduction to {N}umber {T}heory and {A}lgebra},
PUBLISHER = {Cambridge University Press},
ADDRESS = {Cambridge},
YEAR = {2005},
PAGES = {xvi+517},
ISBN = {978-0-521-85154-1; 0-521-85154-8},
MRCLASS = {11-01 (11Y05 11Y11 11Y16)},
MRNUMBER = {MR2151586 (2006g:11003)},
MRREVIEWER = {Jordi Gu{\`a}rdia},
}
@article{ schoof:sqrt,
author={Schoof, R.},
title = {Elliptic Curves Over Finite Fields and the Computation of
Square Roots mod p},
year = {1985},
journal = {Mathematics of Computation},
volume = {44},
number = {170},
pages = {483--494}
}
@book{ mazur-stein:rh,
author = {Mazur, B. and Stein, W.},
title = {What is {R}iemann's {H}ypothesis?},
year = {2008},
note = {In preparation}
}
@Book{ hartshorne,
author = {Hartshorne, R.},
title = {Algebraic {G}eometry},
note = {Graduate Texts in Mathematics, No. 52},
publisher = {Springer-Verlag},
address = {New York},
year = {1977},
pages = {xvi+496},
isbn = {0-387-90244-9}
}
@article{zagier:primes50,
author = {Zagier, D.},
title = {The First 50 Million Prime Numbers},
year = {1975},
note = {{\tt http://modular.fas.harvard.edu/scans/papers/zagier/}}
}
@article {carmichael,
AUTHOR = {Alford, W. R. and Granville, Andrew and Pomerance, Carl},
TITLE = {There are infinitely many {C}armichael numbers},
JOURNAL = {Ann. of Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {139},
YEAR = {1994},
NUMBER = {3},
PAGES = {703--722},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {11N13 (11A07 11A51 11N25)},
MRNUMBER = {95k:11114},
MRREVIEWER = {H. L. Montgomery},
}
@Article{cmi,
author = {{Clay Mathematics Institute}},
title = {Millennium Prize Problems,\hfill\\{\tt
http://www.claymath.org/Millennium\_Prize\_Problems/}}
}
@book {knuth2,
AUTHOR = {Knuth, Donald E.},
TITLE = {The {A}rt of {C}omputer {P}rogramming. {V}ol. 2},
EDITION = {Second},
NOTE = {Seminumerical algorithms,
Addison-Wesley Series in Computer Science and Information
Processing},
PUBLISHER = {Addison-Wesley Publishing Co., Reading, Mass.},
YEAR = {1998},
PAGES = {xiii+762},
ISBN = {0-201-03822-6},
MRCLASS = {68-02 (65-XX 68B05)},
MRNUMBER = {83i:68003},
MRREVIEWER = {M. Muller},
}
@book {knuth1,
AUTHOR = {Knuth, Donald E.},
TITLE = {The {A}rt of {C}omputer {P}rogramming},
EDITION = {Third},
NOTE = {Volume 1: Fundamental algorithms,
Addison-Wesley Series in Computer Science and Information
Processing},
PUBLISHER = {Addison-Wesley Publishing Co., Reading,
Mass.-London-Amsterdam},
YEAR = {1997},
PAGES = {xix+650 pp. (1 table on lining papers)}
}
@article{certicom:challenge,
author = {Certicom},
title = {The Certicom {E}{C}{C} Challenge,
\newline{\tt http://www.certicom.com/\newline{}\mbox{}\qquad{}index.php?action=res,ecc\_challenge}}
}
@article{python,
author = {Rossum, Guido van},
title = {Python,\newline{\tt http://www.python.org}}
}
@book {lenstras:nfs,
TITLE = {The {D}evelopment of the {N}umber {F}ield {S}ieve},
SERIES = {Lecture Notes in Mathematics},
VOLUME = {1554},
EDITOR = {Lenstra, A. K. and Lenstra, Jr., H. W.},
PUBLISHER = {Springer-Verlag},
ADDRESS = {Berlin},
YEAR = {1993},
PAGES = {viii+131},
ISBN = {3-540-57013-6},
MRCLASS = {11Yxx (11-06 11N35 11N36 11Y05 11Y40)},
MRNUMBER = {96m:11116},
MRREVIEWER = {Samuel S. Wagstaff, Jr.},
}
@Article{ wiles:cmi,
author = {Wiles, A.\thinspace{}J.},
title = {The {B}irch and {S}winnerton-{D}yer {C}onjecture},
note = {\\\protect{\tt
http://www.claymath.org/prize\_problems/birchsd.htm}},
year = {2000}
}
@book {engel:problem,
AUTHOR = {Engel, Arthur},
TITLE = {Problem-solving strategies},
SERIES = {Problem Books in Mathematics},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1998},
PAGES = {x+403},
ISBN = {0-387-98219-1},
MRCLASS = {00A07 (05-01)},
MRNUMBER = {98m:00004},
}
@article{sloane,
author = {Sloane, N.\thinspace{}J.\thinspace{}A.},
title = {{T}he {O}n-{L}ine {E}ncyclopedia of {I}nteger {S}equences},
journal = {{\tt http://www.research.att.com/\~{}njas/sequences/}}
}
@article {baum_sweet,
AUTHOR = {Baum, Leonard E. and Sweet, Melvin M.},
TITLE = {Continued fractions of algebraic power series in
characteristic {$2$}},
JOURNAL = {Ann. of Math. (2)},
VOLUME = {103},
YEAR = {1976},
NUMBER = {3},
PAGES = {593--610},
MRCLASS = {10F25},
MRNUMBER = {53 \#13127},
MRREVIEWER = {Thomas W. Cusick},
}
@article{olds:contfrac,
AUTHOR = {Olds, C.\thinspace{}D.},
TITLE = {The {S}imple {C}ontinued {F}raction {E}xpression of $e$},
JOURNAL = {Amer. Math. Monthly},
VOLUME = {77},
PAGES = {968--974},
YEAR = {1970},
}
@article {euler:contfrac,
AUTHOR = {Euler, Leonhard},
TITLE = {An essay on continued fractions},
NOTE = {Translated from the Latin by B.\ F.\ Wyman and M.\ F.\ Wyman},
JOURNAL = {Math. Systems Theory},
FJOURNAL = {Mathematical Systems Theory. An International Journal on
Mathematical Computing Theory},
VOLUME = {18},
YEAR = {1985},
NUMBER = {4},
PAGES = {295--328},
ISSN = {0025-5661},
CODEN = {MASTBA},
MRCLASS = {01A50 (01A75)},
MRNUMBER = {87d:01011b},
MRREVIEWER = {E. J. Barbeau},
}
@article {dh76,
AUTHOR = {Diffie, W. and Hellman, M.\thinspace{}E.},
TITLE = {New directions in cryptography},
JOURNAL = {IEEE Trans. Information Theory},
VOLUME = {IT-22},
YEAR = {1976},
NUMBER = {6},
PAGES = {644--654},
MRCLASS = {94A10},
MRNUMBER = {55 \#10141},
MRREVIEWER = {J. S. Joel},
}
@article{factor576,
author = {Weisstein, E.\thinspace{}W.},
title = {{R}{S}{A}-576 {F}actored, \hfill\\
{\tt http://mathworld.wolfram.com/news/2003-12-05/rsa/}},
year = {2003}
}
@article{quantum15,
AUTHOR = {Vandersypen L.\thinspace{}M. and Steffen M. and Breyta G.
and Yannoni C.\thinspace{}S. and Sherwood M.\thinspace{}H.
and Chuang I.\thinspace{}L.},
title = {Experimental realization of {S}hor's quantum factoring
algorithm using nuclear magnetic resonance},
journal = {Nature},
volume = {414},
year = {2001},
number = {6866},
pages = {883--887}
}
@book {conway:sensual,
AUTHOR = {Conway, John H.},
TITLE = {The {S}ensual ({Q}uadratic) {F}orm},
SERIES = {Carus Mathematical Monographs},
VOLUME = {26},
NOTE = {With the assistance of Francis Y. C. Fung},
PUBLISHER = {Mathematical Association of America},
ADDRESS = {Washington, DC},
YEAR = {1997},
PAGES = {xiv+152},
ISBN = {0-88385-030-3},
MRCLASS = {11E12 (11-01)},
MRNUMBER = {98k:11035},
MRREVIEWER = {Carl Riehm},
}
@book {niven-zuckerman-montgomery,
AUTHOR = {Niven, I. and Zuckerman, H.\thinspace{}S.
and Montgomery, H.\thinspace{}L.},
TITLE = {An {I}ntroduction to the {T}heory of {N}umbers},
EDITION = {Fifth},
PUBLISHER = {John Wiley \& Sons Inc.},
ADDRESS = {New York},
YEAR = {1991},
PAGES = {xiv+529},
ISBN = {0-471-62546-9},
MRCLASS = {11-01},
MRNUMBER = {91i:11001},
}
@book {lorenzini,
AUTHOR = {Lorenzini, D.},
TITLE = {An invitation to arithmetic geometry},
SERIES = {Graduate Studies in Mathematics},
VOLUME = {9},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1996},
PAGES = {xvi+397},
ISBN = {0-8218-0267-4},
MRCLASS = {14G40 (11G20 14-01)},
MRNUMBER = {97e:14035},
MRREVIEWER = {I. Dolgachev},
}
@book {artin,
AUTHOR = {Artin, M.},
TITLE = {Algebra},
PUBLISHER = {Prentice Hall Inc.},
ADDRESS = {Englewood Cliffs, NJ},
YEAR = {1991},
PAGES = {xviii+618},
ISBN = {0-13-004763-5},
MRCLASS = {00A05 (11-01 12-01 13-01 15-01 16-01 20-01)},
MRNUMBER = {92g:00001},
MRREVIEWER = {Gerald J. Janusz},
}
@article{elkies:tables,
AUTHOR = {Elkies, N.},
TITLE = {Algorithmic (a.k.a. {C}omputational) {N}umber {T}heory: {T}ables, {L}inks, etc.\\
{\tt http://www.math.harvard.edu/\~{}elkies/compnt.html}}
}
@book {blake-seroussi-smart,
AUTHOR = {Blake, I. F. and Seroussi, G. and Smart, N. P.},
TITLE = {Elliptic curves in cryptography},
SERIES = {London Mathematical Society Lecture Note Series},
VOLUME = {265},
NOTE = {Reprint of the 1999 original},
PUBLISHER = {Cambridge University Press},
ADDRESS = {Cambridge},
YEAR = {2000},
PAGES = {xvi+204},
ISBN = {0-521-65374-6},
MRCLASS = {94A60 (11G20 14G50)},
MRNUMBER = {2001i:94048},
MRREVIEWER = {Boris {\`E}. Kunyavski{\u\i}},
}
@article{menezes:ecdl,
AUTHOR = {Menezes, A. and Okamoto, T. and Vanstone, S.},
TITLE = {Reducing elliptic curve logarithms to a finite field},
JOURNAL = {IEEEE Trans. Inform. Theory.},
VOLUME = {39},
PAGES = {1639--1646},
YEAR = {1993}
}
@article {smart:ecdl,
AUTHOR = {Smart, N. P.},
TITLE = {The discrete logarithm problem on elliptic curves of trace
one},
JOURNAL = {J. Cryptology},
FJOURNAL = {Journal of Cryptology. The Journal of the International
Association for Cryptologic Research},
VOLUME = {12},
YEAR = {1999},
NUMBER = {3},
PAGES = {193--196},
ISSN = {0933-2790},
CODEN = {JOCREQ},
MRCLASS = {11G20 (11T71 94A60)},
MRNUMBER = {2000b:11069}
}
@book {cohn:advanced,
AUTHOR = {Cohn, H.},
TITLE = {Advanced number theory},
NOTE = {Reprint of {\it A second course in number theory}, 1962,
Dover Books on Advanced Mathematics},
PUBLISHER = {Dover Publications Inc.},
ADDRESS = {New York},
YEAR = {1980},
PAGES = {xi+276},
ISBN = {0-486-64023-X},
MRCLASS = {12-01 (10-02)},
MRNUMBER = {82b:12001}
}
@book {cassels:lectures,
AUTHOR = {Cassels, J. W. S.},
TITLE = {Lectures on elliptic curves},
SERIES = {London Mathematical Society Student Texts},
VOLUME = {24},
PUBLISHER = {Cambridge University Press},
ADDRESS = {Cambridge},
YEAR = {1991},
PAGES = {vi+137},
ISBN = {0-521-41517-9; 0-521-42530-1},
MRCLASS = {11G05 (14H52)},
MRNUMBER = {92k:11058},
MRREVIEWER = {Philippe Satg{\'e}}
}
@article{twins,
author={Caldwell, C.},
title={The {T}op {T}wenty {T}win {P}rimes\\
{\tt http://www.utm.edu/research/primes/lists/top20/twin.html}}
}
@article{richstein:goldbach,
author = {Richstein, J.},
title = {Verifying {G}oldbach's {C}onjecture up to $4\cdot 10^{14}$,\\
{\tt http://www.informatik.uni-giessen.de/staff/richstein/\\ca/Goldbach.html}}
}
@book {petros,
AUTHOR = {Doxiadis, A.},
TITLE = {Uncle {P}etros and {G}oldbach's conjecture},
NOTE = {Translated by the author from the 1992 Greek original},
PUBLISHER = {Bloomsbury, New York},
YEAR = {2000},
PAGES = {iv+213},
ISBN = {1-58234-067-6},
MRCLASS = {01A99 (00A08 11-03 11P32)},
MRNUMBER = {2002c:01050},
MRREVIEWER = {Lawrence Somer},
}
@incollection {birch:atkin,
AUTHOR = {Birch, B.},
TITLE = {Atkin and the {A}tlas {L}ab},
BOOKTITLE = {Computational perspectives on number theory (Chicago, IL,
1995)},
SERIES = {AMS/IP Stud. Adv. Math.},
VOLUME = {7},
PAGES = {13--20},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1998},
MRCLASS = {11-03 (01A60 11F30 11F33)},
MRNUMBER = {99c:11002},
MRREVIEWER = {V. Kumar Murty},
}
@proceedings {MR98g:11001,
TITLE = {Computational perspectives on number theory},
SERIES = {AMS/IP Studies in Advanced Mathematics},
VOLUME = {7},
BOOKTITLE = {Proceedings of the conference in honor of A. O. L. Atkin held
at the University of Illinois, Chicago, IL, September 1995},
EDITOR = {Buell, D. A. and Teitelbaum, J. T.},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1998},
PAGES = {x+232},
ISBN = {0-8218-0880-X},
MRCLASS = {11-01 (00B30 11Yxx)},
MRNUMBER = {98g:11001},
}
@article{taylor-wiles:fermat,
AUTHOR = {Taylor, R. and Wiles, A.\thinspace{}J.},
TITLE = {Ring-theoretic properties of certain \protect{H}ecke algebras},
JOURNAL = {Ann. of Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {141},
YEAR = {1995},
NUMBER = {3},
PAGES = {553--572},
ISSN = {0003-486X},
CODEN = {ANMAAH},
}
@article{ribet-hayes:flt,
AUTHOR = {Ribet, K. and Hayes, B.},
TITLE = {{F}ermat's {L}ast {T}heorem and {M}odern {A}rithmetic},
JOURNAL = {American Scientist},
YEAR = {March--April, 1994}
}
@article {ribet:galoissurvey,
AUTHOR = {Ribet, K.\thinspace{}A.},
TITLE = {Galois representations and modular forms},
JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
FJOURNAL = {American Mathematical Society. Bulletin. New Series},
VOLUME = {32},
YEAR = {1995},
NUMBER = {4},
PAGES = {375--402},
ISSN = {0273-0979},
CODEN = {BAMOAD},
}
@book {alf:flt,
AUTHOR = {van der Poorten, A.},
TITLE = {Notes on {F}ermat's last theorem},
SERIES = {Canadian Mathematical Society Series of Monographs and
Advanced Texts},
NOTE = {A Wiley-Interscience Publication},
PUBLISHER = {John Wiley \& Sons Inc.},
ADDRESS = {New York},
YEAR = {1996},
PAGES = {xviii+222},
ISBN = {0-471-06261-8},
MRCLASS = {11D41 (00A08 01A05 11-03)},
MRNUMBER = {98c:11026},
}
@book {singh:enigma,
AUTHOR = {Singh, S.},
TITLE = {Fermat's enigma},
NOTE = {The epic quest to solve the world's greatest mathematical
problem,
With a foreword by John Lynch},
PUBLISHER = {Walker and Company, New York},
YEAR = {1997},
PAGES = {xx+315},
ISBN = {0-8027-1331-9},
MRCLASS = {01A05 (01A70 11-03)},
MRNUMBER = {98i:01001},
MRREVIEWER = {Andrew Bremner},
}
@article {merel,
AUTHOR = {Merel, L.},
TITLE = {Bornes pour la torsion des courbes elliptiques sur les corps
de nombres},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {124},
YEAR = {1996},
NUMBER = {1-3},
PAGES = {437--449},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {11G05 (11L05)},
MRNUMBER = {96i:11057},
MRREVIEWER = {Henri Darmon},
}
@article{cremona:onlinetables,
author = {Cremona, J.\thinspace{}E.},
title = {Elliptic curves of conductor \protect{$\leq 17000$},\hfill\\
{\tt http://www.maths.nott.ac.uk/personal/jec/ftp/data/}}
}
@book{cremona:algs,
AUTHOR = {Cremona, J.\thinspace{}E.},
TITLE = {Algorithms for modular elliptic curves},
EDITION = {Second},
PUBLISHER = {Cambridge University Press},
ADDRESS = {Cambridge},
YEAR = {1997},
PAGES = {vi+376},
ISBN = {0-521-59820-6},
}
@article{mwrank,
author = {Cremona, J.\thinspace{}E.},
title = {{\tt mwrank} (computer software)},
journal = {\\{\tt http://www.maths.nott.ac.uk/personal/jec/ftp/progs/}}
}
@book {koblitz:cong,
AUTHOR = {Koblitz, N.},
TITLE = {Introduction to {E}lliptic {C}urves and {M}odular {F}orms},
SERIES = {Graduate Texts in Mathematics},
VOLUME = {97},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1984},
PAGES = {viii+248},
ISBN = {0-387-96029-5},
MRCLASS = {11G05 (11G40 14G25 14K07)},
MRNUMBER = {86c:11040},
MRREVIEWER = {Leslie Jane Federer},
}
@article {gross-zagier,
author = {Gross, B. and Zagier, D.},
TITLE = {Heegner points and derivatives of \protect{${L}$}-series},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {84},
YEAR = {1986},
NUMBER = {2},
PAGES = {225--320},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {11G40 (11F11 11G05 14G10)},
MRNUMBER = {87j:11057},
MRREVR = {Loren D. Olson},
}
@article{cohn:contfrac,
AUTHOR={Cohn, H.},
TITLE = {A short proof of the continued fraction expansion of $e$,\\{\tt http://research.microsoft.com/\~{}cohn/publications.html}}
}
@book {perron,
AUTHOR = {Perron, O.},
TITLE = {Die {L}ehre von den {K}ettenbr\"uchen. {D}ritte, verbesserte
und erweiterte {A}ufl. {B}d. {II}.
{A}nalytisch-funktionentheoretische {K}ettenbr\"uche},
PUBLISHER = {B. G. Teubner Verlagsgesellschaft, Stuttgart},
YEAR = {1957},
PAGES = {vi+316},
MRCLASS = {30.0X},
MRNUMBER = {19,25c},
MRREVIEWER = {E. Frank},
}
@article{weisstein,
AUTHOR = {Weisstein, E.},
TITLE = {Eric Weisstein's World of Mathematics},
YEAR = {2003},
JOURNAL = {{\tt http://mathworld.wolfram.com}}
}
@article{nova:proof,
AUTHOR = {Singh, S.},
TITLE = {The {P}roof},
YEAR = {1997},
JOURNAL={\mbox{}\\{\tt http://www.pbs.org/wgbh/nova/transcripts/2414proof.html}}
}
@article {wiles:fermat,
AUTHOR = {Wiles, A.\thinspace{}J.},
TITLE = {Modular elliptic curves and \protect{F}ermat's last theorem},
JOURNAL = {Ann. of Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {141},
YEAR = {1995},
NUMBER = {3},
PAGES = {443--551},
ISSN = {0003-486X},
CODEN = {ANMAAH},
}
@article {ribet:modreps,
AUTHOR = {Ribet, K.\thinspace{}A.},
TITLE = {On modular representations of
\protect{${\rm {G}al}(\overline{\bf{Q}}/{\bf {Q}})$}
arising from modular forms},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {100},
YEAR = {1990},
NUMBER = {2},
PAGES = {431--476},
ISSN = {0020-9910},
CODEN = {INVMBH},
}
@article {coates-wiles:bsd,
AUTHOR = {Coates, J. and Wiles, A.},
TITLE = {On the conjecture of {B}irch and {S}winnerton-{D}yer},
JOURNAL = {Invent. Math.},
VOLUME = {39},
YEAR = {1977},
NUMBER = {3},
PAGES = {223--251},
MRCLASS = {14G10 (10D15 14G25)},
MRNUMBER = {57 \#3134},
MRREVIEWER = {Kenneth A. Ribet},
}
@article {magma,
AUTHOR = {Bosma, W. and Cannon, J. and Playoust, C.},
TITLE = {The {M}agma algebra system. {I}. {T}he user language},
NOTE = {Computational algebra and number theory (London, 1993)},
JOURNAL = {J. Symbolic Comput.},
FJOURNAL = {Journal of Symbolic Computation},
VOLUME = {24},
YEAR = {1997},
NUMBER = {3-4},
PAGES = {235--265},
ISSN = {0747-7171},
MRCLASS = {68Q40},
MRNUMBER = {1 484 478},
}
@incollection{diamond-im,
AUTHOR = {Diamond, F. and Im, J.},
TITLE = {Modular forms and modular curves},
BOOKTITLE = {Seminar on {F}ermat's {L}ast {T}heorem},
PAGES = {39--133},
ppPUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1995},
}
@book {MR96f:11004,
TITLE = {Seminar on {F}ermat's {L}ast {T}heorem},
EDITOR = {Murty, V. Kumar},
NOTE = {Papers from the seminar held at the Fields Institute for
Research in Mathematical Sciences, Toronto, Ontario,
1993--1994},
PUBLISHER = {Published by the American Mathematical Society, Providence, RI},
YEAR = {1995},
PAGES = {x+265},
ISBN = {0-8218-0313-1},
MRCLASS = {11-06 (11D41 11G05 11G18)},
MRNUMBER = {96f:11004},
}
@book {serre:arithmetic,
AUTHOR = {Serre, J-P.},
TITLE = {A \protect{C}ourse in \protect{A}rithmetic},
NOTE = {Translated from the French,
Graduate Texts in Mathematics, No. 7},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1973},
PAGES = {viii+115},
}
@book {silvermantate,
AUTHOR = {Silverman, J.\thinspace{}H. and Tate, J.},
TITLE = {Rational points on elliptic curves},
SERIES = {Undergraduate Texts in Mathematics},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1992},
PAGES = {x+281},
ISBN = {0-387-97825-9},
MRCLASS = {11-01 (11D25 11G05 14H52)},
MRNUMBER = {93g:11003},
MRREVIEWER = {Andrew Bremner},
}
@article {lenstra:factorell,
AUTHOR = {Lenstra, Jr., H.\thinspace{}W.},
TITLE = {Factoring integers with elliptic curves},
JOURNAL = {Ann. of Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {126},
YEAR = {1987},
NUMBER = {3},
PAGES = {649--673},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {11Y05 (11A51 14K07)},
MRNUMBER = {89g:11125},
MRREVIEWER = {Hale F. Trotter},
}
@article{rank24,
AUTHOR = {Martin, R. and McMillen W.},
TITLE = {An {E}lliptic {C}urve over {$\Q$} with {R}ank at least 24},
YEAR = {2000},
JOURNAL = {\mbox{}\\{\tt http://listserv.nodak.edu/scripts/wa.exe?A2=ind0005\&\\{}L=nmbrthry\&P=R182}}
}
@book {silverman:aec,
AUTHOR = {Silverman, J.\thinspace{}H.},
TITLE = {The arithmetic of elliptic curves},
SERIES = {Graduate Texts in Mathematics},
VOLUME = {106},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1986},
PAGES = {xii+400},
ISBN = {0-387-96203-4},
MRCLASS = {11G05 (14Gxx 14K07 14K15)},
MRNUMBER = {87g:11070},
MRREVIEWER = {Robert S. Rumely},
}
@book {halmos:naive,
AUTHOR = {Halmos, P.\thinspace{}R.},
TITLE = {Naive set theory},
SERIES = {The University Series in Undergraduate Mathematics},
PUBLISHER = {D. Van Nostrand Co., Princeton, N.J.-Toronto-London-New York},
YEAR = {1960},
PAGES = {vii+104},
MRCLASS = {04.00},
MRNUMBER = {22 \#5575},
MRREVIEWER = {L. Rieger},
}
@book {ahlfors,
AUTHOR = {Ahlfors, L.\thinspace{}V.},
TITLE = {Complex {A}nalysis},
EDITION = {Third},
NOTE = {An introduction to the theory of analytic functions of one
complex variable,
International Series in Pure and Applied Mathematics},
PUBLISHER = {McGraw-Hill Book Co.},
ADDRESS = {New York},
YEAR = 1978,
PAGES = {xi+331},
ISBN = {0-07-000657-1},
MRCLASS = {30-01},
MRNUMBER = {80c:30001},
}
@article {cassels:arith4,
AUTHOR = {Cassels, J.\thinspace{}W.\thinspace{}S.},
TITLE = {Arithmetic on {C}urves of {G}enus \protect{$1$}. {I}{V}.
{P}roof of the {H}auptvermutung},
JOURNAL = {J. Reine Angew. Math.},
VOLUME = {211},
YEAR = {1962},
PAGES = {95--112},
}
@book {wall,
AUTHOR = {Wall, H. S.},
TITLE = {Analytic {T}heory of {C}ontinued {F}ractions},
PUBLISHER = {D. Van Nostrand Company, Inc., New York, N. Y.},
YEAR = {1948},
PAGES = {xiii+433},
MRCLASS = {40.0X},
MRNUMBER = {10,32d},
MRREVIEWER = {R. C. Buck},
}
@book {stark,
AUTHOR = {Stark, H.\thinspace{}M.},
TITLE = {An introduction to number theory},
PUBLISHER = {MIT Press},
ADDRESS = {Cambridge, Mass.},
YEAR = {1978},
PAGES = {x+347},
ISBN = {0-262-69060-8},
MRCLASS = {10-01},
MRNUMBER = {80a:10001},
}
@article {lenstra:pell,
AUTHOR = {Lenstra, Jr., H.\thinspace{}W.},
TITLE = {Solving the {P}ell equation},
JOURNAL = {Notices Amer. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical Society},
VOLUME = {49},
YEAR = {2002},
NUMBER = {2},
PAGES = {182--192},
ISSN = {0002-9920},
CODEN = {AMNOAN},
MRCLASS = {11D09 (01A99 11R27)},
MRNUMBER = {2002i:11028},
MRREVIEWER = {Duncan A. Buell}
}
@book {cohen:ant,
AUTHOR = {Cohen, H.},
TITLE = {A {C}ourse in {C}omputational {A}lgebraic {N}umber {T}heory},
SERIES = {Graduate Texts in Mathematics},
VOLUME = {138},
PUBLISHER = {Springer-Verlag},
ADDRESS = {Berlin},
YEAR = {1993},
PAGES = {xii+534},
ISBN = {3-540-55640-0},
MRCLASS = {11Y40 (11Rxx 68Q40)},
MRNUMBER = {94i:11105},
MRREVIEWER = {Joe P. Buhler}
}
@article {langtrotter1,
AUTHOR = {Lang, S. and Trotter, H.},
TITLE = {Continued fractions for some algebraic numbers},
JOURNAL = {J. Reine Angew. Math.},
VOLUME = {255},
YEAR = {1972},
PAGES = {112--134; addendum, ibid. {\bf 267} (1974), 219--220; MR {\bf
50} \#2086},
MRCLASS = {10F20},
MRNUMBER = {46 \#5258},
MRREVIEWER = {R. Guting}
}
@article {langtrotter2,
AUTHOR = {Lang, S. and Trotter, H.},
TITLE = {Addendum to: {C}ontinued fractions for some algebraic
numbers ({J}. {R}eine {A}ngew. {M}ath. {\bf 255}\ (1972),
112--134)},
JOURNAL = {J. Reine Angew. Math.},
VOLUME = {267},
YEAR = {1974},
PAGES = {219--220},
MRCLASS = {10F20},
MRNUMBER = {50 \#2086},
MRREVIEWER = {R. Guting}
}
@book {khintchine,
AUTHOR = {Khintchine, A. Ya.},
TITLE = {Continued fractions},
SERIES = {Translated by Peter Wynn},
PUBLISHER = {P. Noordhoff Ltd.},
ADDRESS = {Groningen},
YEAR = {1963},
PAGES = {iii+101},
MRCLASS = {10.31},
MRNUMBER = {28 \#5038},
MRREVIEWER = {E. Frank}
}
@book {davenport,
AUTHOR = {Davenport, H.},
TITLE = {The {H}igher {A}rithmetic},
EDITION = {Seventh},
NOTE = {An introduction to the theory of numbers,
Chapter VIII by J. H. Davenport},
PUBLISHER = {Cambridge University Press},
ADDRESS = {Cambridge},
YEAR = {1999},
PAGES = {241},
ISBN = {0-521-63446-6},
MRCLASS = {11-01},
MRNUMBER = {2000k:11002}
}
@book {burton,
AUTHOR = {Burton, D.\thinspace{}M.},
TITLE = {Elementary {N}umber {T}heory},
EDITION = {Second},
PUBLISHER = {W. C. Brown Publishers},
ADDRESS = {Dubuque, IA},
YEAR = {1989},
PAGES = {xviii+450},
ISBN = {0-697-05919-7},
MRCLASS = {11-01},
MRNUMBER = {90e:11001},
MRREVIEWER = {Harvey Cohn}
}
@book {hardywright,
AUTHOR = {Hardy, G.\thinspace{}H. and Wright, E.\thinspace{}M.},
TITLE = {An {I}ntroduction to the {T}heory of {N}umbers},
EDITION = {Fifth},
PUBLISHER = {The Clarendon Press Oxford University Press},
ADDRESS = {New York},
YEAR = {1979},
PAGES = {xvi+426},
ISBN = {0-19-853170-2; 0-19-853171-0},
MRCLASS = {10-01},
MRNUMBER = {81i:10002},
MRREVIEWER = {T. M. Apostol}
}
@article{dunne,
AUTHOR = {Dunne, E.\thinspace{}G.},
TITLE = {{P}ianos and {C}ontinued {F}ractions},
JOURNAL = {{\tt http://www.research.att.com/\~{}njas/sequences/\newline{}DUNNE/TEMPERAMENT.HTML}}
}
@article {hooley:artin,
AUTHOR = {Hooley, C.},
TITLE = {On {A}rtin's conjecture},
JOURNAL = {J. Reine Angew. Math.},
VOLUME = {225},
YEAR = {1967},
PAGES = {209--220},
MRCLASS = {10.66 (10.41)},
MRNUMBER = {34 \#7445},
MRREVIEWER = {Werner G. H. Schaal},
}
@book {ireland-rosen,
AUTHOR = {Ireland, K. and Rosen, M.},
TITLE = {A {C}lassical {I}ntroduction to {M}odern {N}umber {T}heory},
EDITION = {Second},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1990},
PAGES = {xiv+389},
ISBN = {0-387-97329-X},
MRCLASS = {11-01 (11-02)},
MRNUMBER = {92e:11001},
MRREVIEWER = {Glenn Stevens},
}
@article{qrlist,
AUTHOR={Lemmermeyer, F.},
TITLE={Proofs of the {Q}uadratic {R}eciprocity {L}aw,\\{\tt http://www.rzuser.uni-heidelberg.de/\~{}hb3/rchrono.html}}
}
@article {pieter:artin,
AUTHOR = {Moree, P.},
TITLE = {A note on {A}rtin's conjecture},
JOURNAL = {Simon Stevin},
FJOURNAL = {Simon Stevin. A Quarterly Journal of Pure and Applied
Mathematics},
VOLUME = {67},
YEAR = {1993},
NUMBER = {3-4},
PAGES = {255--257},
ISSN = {0037-5454},
CODEN = {SSWNAX},
MRCLASS = {11N69},
MRNUMBER = {95e:11106},
MRREVIEWER = {D. R. Heath-Brown},
}
@book{singh:crypto,
AUTHOR = {Singh, S.},
TITLE = {The {C}ode {B}ook: {T}he {S}cience of {S}ecrecy from {A}ncient {E}gypt to {Q}uantum {C}ryptography},
YEAR = {1999},
PUBLISHER = {Doubleday},
ISBN = {0-385-49531-5}
}
@article{agrawal:primes,
AUTHOR ={Agrawal, M. and Kayal, N. and Saxena, N.},
TITLE = {{PRIMES} is in {$P$}},
journal = {to appear in Annals of Math.,
\\{\tt http://www.cse.iitk.ac.in/users/manindra/primality.ps}},
YEAR = {2002}
}