Symmetric square L-function bug for odd chi

[loefflerd]

This is a followup to #19668 which added functionality for computing symmetric square L-functions of modular forms (via the Sage interface to Dokchitser's ComputeL GP/PARI script). Unfortunately, the code has a bug when the twisting character psi has non-real values, as one can see by checking the functional equation.

sage: F = Newforms(1,12)[0]
sage: chi = DirichletGroup(7).0
sage: F.symsquare_lseries(chi^2).check_functional_equation() # even char
-9.06002242118120e-8 - 1.94297172129154e-7*I
sage: F.symsquare_lseries(chi).check_functional_equation() # odd char
8.86658506905467e7 + 1.10964024593305e8*I

Note the huge discrepancy for the odd character. This is because the Gamma and epsilon factor parameters are being computed wrongly. (Thanks to Jim Brown for pointing this out)

Component: modular forms

Keywords: L-functions

Author: David Loeffler

Branch: 390030b

Reviewer: Frédéric Chapoton, Jim Brown

Issue created by migration from https://trac.sagemath.org/ticket/23247

[loefflerd]

Branch: public/23247/symmetric_square_l_function_bug_for_odd_chi

[loefflerd]

comment:2

Here's a patch.

---

New commits:

9bd5650

Trac #23247: fixed gamma and epsilon factors for chi odd

[loefflerd]

Commit: 9bd5650

[loefflerd]

Author: David Loeffler

[fchapoton]

Changed commit from 9bd5650 to 390030b

[fchapoton]

Reviewer: Frédéric Chapoton

[fchapoton]

Changed branch from public/23247/symmetric_square_l_function_bug_for_odd_chi to public/23247-lfunction

[fchapoton]

comment:4

Looks good to me. I made a tiny cosmetic change. If you agree with it, you can set to positive on my behalf.

---

New commits:

390030b

trac 23247 some details

[loefflerd]

comment:5

Great, thanks!

[sagetrac-jbrown]

comment:6

I have used the new code and it works correctly now. It is a positive review from me.

[vbraun]

Changed branch from public/23247-lfunction to 390030b

[loefflerd]

comment:8

I've added Jim's name as reviewer.

[loefflerd]

Changed commit from 390030b to none

[loefflerd]

Changed reviewer from Frédéric Chapoton to Frédéric Chapoton, Jim Brown