# Ticket #1287(closed enhancement: fixed)

Opened 6 years ago

## [with patch, with *positive* review] wrappers for Dokchitser L-series

Reported by: Owned by: jen was major sage-2.8.15 number theory

### 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
```

## Change History

### comment:1 Changed 6 years ago by was

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.

### comment:2 Changed 6 years ago by mabshoff

• Summary changed from [with patch] wrappers for Dokchitser L-series to [with patch, with negative review] wrappers for Dokchitser L-series

### comment:3 Changed 6 years ago by was

• 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 6 years ago by mabshoff

• Status changed from new to closed
• Resolution set to fixed

Merged in 2.8.15.rc0.

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