Closed jbalakrishnan closed 16 years ago
Attachment: patch.hg.gz
Unfortunately there is a bug somewhere or some sort of mathematical contradiction going on here, as the following calculation illustrates:
sage: M = ModularSymbols(1,12)
sage: d = M.cuspidal_submodule().rational_period_mapping()
sage: for i in range(11):
... print i, d(M.modular_symbol((i, 0,oo)))
0 (1620/691, 0)
1 (0, 1)
2 (-1, 0)
3 (0, -25/48)
4 (9/14, 0)
5 (0, 5/12)
6 (-9/14, 0)
7 (0, -25/48)
8 (1, 0)
9 (0, 1)
10 (-1620/691, 0)
sage: L = eisenstein_series_Lseries(12)
sage: L(3)
2.89830333000000e-17
sage: L(5)
7.35601685000000e-17
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.
Doh -- I was being stupid / confused between Eisenstein series and cusp form, since it was a long day.
Change this to a positive review!
Merged in 2.8.15.rc0.
Wrappers for Dokchitser L-series for various types of modular forms, e.g.,:
Component: number theory
Issue created by migration from https://trac.sagemath.org/ticket/1287