Opened 9 years ago
Closed 9 years ago
#1287 closed enhancement (fixed)
[with patch, with *positive* review] wrappers for Dokchitser L-series
Reported by: | jen | Owned by: | was |
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Priority: | major | Milestone: | sage-2.8.15 |
Component: | number theory | Keywords: | |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Wrappers for Dokchitser L-series for various types of modular forms, e.g.,:
sage: L = delta_Lseries() sage: L(1) 0.0374412812685155 sage: f = CuspForms(2,8).0 sage: L = f.cuspform_Lseries() sage: L(1) 0.0884317737041015 sage: L(0.5) 0.0296568512531983 sage: f = ModularForms(1,4).0 sage: L = f.modform_Lseries() sage: L(1) -0.0304484570583933 sage: L = eisenstein_series_Lseries(20) sage: L(2) -5.02355351645987
Attachments (1)
Change History (5)
Changed 9 years ago by
comment:1 Changed 9 years ago by
comment:2 Changed 9 years ago by
- Summary changed from [with patch] wrappers for Dokchitser L-series to [with patch, with negative review] wrappers for Dokchitser L-series
comment:3 Changed 9 years ago by
- Summary changed from [with patch, with negative review] wrappers for Dokchitser L-series to [with patch, with *positive* review] wrappers for Dokchitser L-series
*Doh* -- I was being stupid / confused between Eisenstein series and cusp form, since it was a long day.
Change this to a positive review!
comment:4 Changed 9 years ago by
- Resolution set to fixed
- Status changed from new to closed
Merged in 2.8.15.rc0.
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Unfortunately there is a bug somewhere or some sort of mathematical contradiction going on here, as the following calculation illustrates:
The modular symbols calculation verifies that L(i) for odd integers i=3,5, etc. is nonzero. This also agrees with the Riemann Hypothesis for L(Delta, s). However, for some strange reason the Dokchitser L that you're computing is 0 at some odd integers. This means there is something wrong.
I haven't figured out what yet. I'll let Jen see if she can.
This can't go in sage as is though.