Opened 4 years ago

Closed 4 years ago

Last modified 4 years ago

#23247 closed defect (fixed)

Symmetric square L-function bug for odd chi

Reported by: davidloeffler Owned by:
Priority: minor Milestone: sage-8.0
Component: modular forms Keywords: L-functions
Cc: Merged in:
Authors: David Loeffler Reviewers: Frédéric Chapoton, Jim Brown
Report Upstream: N/A Work issues:
Branch: 390030b (Commits) Commit:
Dependencies: Stopgaps:

Description

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)

Change History (8)

comment:1 Changed 4 years ago by davidloeffler

  • Branch set to public/23247/symmetric_square_l_function_bug_for_odd_chi

comment:2 Changed 4 years ago by davidloeffler

  • Commit set to 9bd5650836d8ef3e0cb50cfaebc558f0fcf379c4
  • Status changed from new to needs_review

Here's a patch.

New commits:

​9bd5650Trac #23247: fixed gamma and epsilon factors for chi odd

comment:3 Changed 4 years ago by davidloeffler

  • Authors set to David Loeffler

comment:4 Changed 4 years ago by chapoton

  • Branch changed from public/23247/symmetric_square_l_function_bug_for_odd_chi to public/23247-lfunction
  • Commit changed from 9bd5650836d8ef3e0cb50cfaebc558f0fcf379c4 to 390030b29b950c40248e96adca1a1dc49c2ee8db
  • Reviewers set to Frédéric Chapoton

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:

​390030btrac 23247 some details

comment:5 Changed 4 years ago by davidloeffler

  • Status changed from needs_review to positive_review

Great, thanks!

comment:6 Changed 4 years ago by jbrown

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

comment:7 Changed 4 years ago by vbraun

  • Branch changed from public/23247-lfunction to 390030b29b950c40248e96adca1a1dc49c2ee8db
  • Resolution set to fixed
  • Status changed from positive_review to closed

comment:8 Changed 4 years ago by davidloeffler

  • Commit 390030b29b950c40248e96adca1a1dc49c2ee8db deleted
  • Reviewers changed from Frédéric Chapoton to Frédéric Chapoton, Jim Brown

I've added Jim's name as reviewer.

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