gauss_sum mod1

[nsirolli]

The implementation for the Gauss sum for a character chi does include the value chi(0). This is correct for every character except for the character modulo 1. In this case, the output for the Gauss sum equals zero, but it should be 1.

This issue is fixed by adding the value chi(0) to the Gauss sum.

Component: modular forms

Keywords: Gauss sum trivial character

Author: Nicolás Sirolli

Branch/Commit: 6e69aa6

Reviewer: Michalis Neururer

Merged: 8.2.rc1

Issue created by migration from https://trac.sagemath.org/ticket/25127

[nsirolli]

Branch: u/nmsirolli/gauss_sum_mod1

[nsirolli]

Commit: 0ce4c53

[nsirolli]

Changed keywords from none to Gauss sum trivial character

[nsirolli]

Author: Nicolás Sirolli

[nsirolli]

Merged: 8.2.rc1

[alexjbest]

comment:3

Wouldn't instead changing the line below to for c in chi.values(): by removing the [1:] have the same effect and be neater?

Also if this is changed gauss_sum_numerical probably should be too.

[sagetrac-mneururer]

comment:4

I changed the loop to a loop over chi.values() and also changed gauss_sum_numerical as requested by alexjbest.

[sagetrac-mneururer]

Changed branch from u/nmsirolli/gauss_sum_mod1 to u/mneururer/gauss_sum_mod1

[sagetrac-mneururer]

Changed commit from 0ce4c53 to d5bc861

[sagetrac-mneururer]

Changed author from Nicolás Sirolli to Nicolás Sirolli, Michael Neururer

[sagetrac-mneururer]

Changed author from Nicolás Sirolli, Michael Neururer to Nicolás Sirolli, Michalis Neururer

[sagetrac-mneururer]

Reviewer: Michalis Neururer

[sagetrac-mneururer]

Changed author from Nicolás Sirolli, Michalis Neururer to Nicolás Sirolli

[nsirolli]

comment:7

Replying to @alexjbest:

Wouldn't instead changing the line below to for c in chi.values(): by removing the [1:] have the same effect and be neater?

Also if this is changed gauss_sum_numerical probably should be too.

This looks neater, but in the final iteration it computes the product z *= zeta, which is not needed. That's why I did not propose this solution.

[sagetrac-git]

Changed commit from d5bc861 to 6e69aa6

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

31fdc6b	Reverted my changes and corrected gauss_sum_numerical
6e69aa6	Improved code

[vbraun]

Changed branch from u/mneururer/gauss_sum_mod1 to 6e69aa6