#23247 closed defect (fixed)
Symmetric square Lfunction bug for odd chi
Reported by:  davidloeffler  Owned by:  

Priority:  minor  Milestone:  sage8.0 
Component:  modular forms  Keywords:  Lfunctions 
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 Lfunctions 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 nonreal 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 9.06002242118120e8  1.94297172129154e7*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
 Branch set to public/23247/symmetric_square_l_function_bug_for_odd_chi
comment:2 Changed 4 years ago by
 Commit set to 9bd5650836d8ef3e0cb50cfaebc558f0fcf379c4
 Status changed from new to needs_review
comment:3 Changed 4 years ago by
comment:4 Changed 4 years ago by
 Branch changed from public/23247/symmetric_square_l_function_bug_for_odd_chi to public/23247lfunction
 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:
390030b  trac 23247 some details

comment:6 Changed 4 years ago by
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
 Branch changed from public/23247lfunction to 390030b29b950c40248e96adca1a1dc49c2ee8db
 Resolution set to fixed
 Status changed from positive_review to closed
comment:8 Changed 4 years ago by
 Commit 390030b29b950c40248e96adca1a1dc49c2ee8db deleted
 Reviewers changed from Frédéric Chapoton to Frédéric Chapoton, Jim Brown
I've added Jim's name as reviewer.
Here's a patch.
New commits:
Trac #23247: fixed gamma and epsilon factors for chi odd