Opened 4 years ago

Closed 4 years ago

#20254 closed defect (fixed)

Improvements on p-adic L-functions for elliptic curves

Reported by: wuthrich Owned by:
Priority: minor Milestone: sage-7.2
Component: elliptic curves Keywords: days71, p-adic L-functions
Cc: roed Merged in:
Authors: Chris Wuthrich Reviewers: Julian Rüth
Report Upstream: N/A Work issues:
Branch: f29d685 (Commits) Commit: f29d68508ffcaa40aadbfa1a6594633fdf388094
Dependencies: Stopgaps:

Description

There are a few issues about p-adic L-function for elliptic curves. One is that the coefficient ring of supersingular series should be an p-adic Eisenstein field rather than a quotient field.

Change History (27)

comment:1 Changed 4 years ago by wuthrich

  • Keywords days71 added

comment:2 Changed 4 years ago by saraedum

  • Cc roed added

comment:3 Changed 4 years ago by roed

  • Summary changed from Improvments on p-adic L-functions for elliptic curves to Improvements on p-adic L-functions for elliptic curves

Is the coefficient ring issue resolved by #20244? What other changes should be made for p-adic L-functions of elliptic curves?

comment:4 Changed 4 years ago by wuthrich

Oh, there is a lot to do, I discovered. The #20244 will be independent as I will call extension directly rather than root_field.

The main issue is the normalisation for p-adic L-function involving negative modular symbols. They are used when a quadratic twist is used and that happens even for E.sha().an_padic(p). I am close to resolving this.

The major outstanding issue that I will not change here is #4656 which makes some coefficients (with negative precision sometimes) disappear from the series.

comment:5 Changed 4 years ago by wuthrich

  • Branch set to /u/wuthrich/ticket/20254
  • Commit set to 45297356bc88459869d18fc16f2acee7bff60131

New commits:

9f6b4e8trac 20254: changing supersingular p-adic L-series to use Eisenstein p-adics rather than quotient rings
7d1232ctrac 20254 : correcting the normalisation of negative modular symbols
4529735trac 20254: some doctests adjustments

comment:6 Changed 4 years ago by wuthrich

  • Commit changed from 45297356bc88459869d18fc16f2acee7bff60131 to a265fc0f458017a32e6a923b836901a8baaaf3c0
  • Status changed from new to needs_review

This is ready for review.

Apart from cosmetic changes in documentation and code, this does the following

  • The negative modular symbols are now correctly normalised. [r]^- is the quotient of the imaginary part of 2 pi i int_oo^0 f(z)dz by the imaginary part of the period on the imaginary axis with smallest positive imaginary part.
  • The output of a series for a supersingular p-adic L-function is now an element in the Eisenstein ring generated by the root of the Frobenius polynomial. In particular, they are printed alpha-adically.

New commits:

6677b7btrac 20254: further small adjustments to twists in padic lseries
139514fMerge branch 'develop' into oxford
1a7a261trac 20254: correcting small errors
a265fc0trac 20254: final doctests adjustments

comment:7 Changed 4 years ago by saraedum

Some minor remarks:

  • You added a few chunks of commented out code. These should be removed I guess. If they can't then there should at least be a comment what they are about.
  • _poly() has no complete docstring (in particular no doctests)
  • You need to set your author in the ticket

Without understanding all the details, everything else seems alright. Feel free to set to postitive review yourself once you adressed the above.

Last edited 4 years ago by saraedum (previous) (diff)

comment:8 Changed 4 years ago by saraedum

  • Reviewers set to Julian Rüth

comment:9 Changed 4 years ago by saraedum

  • Status changed from needs_review to needs_work

comment:10 Changed 4 years ago by wuthrich

  • Authors changed from wuthrich to Chris Wuthrich
  • Commit changed from a265fc0f458017a32e6a923b836901a8baaaf3c0 to 8b7674311465d1a604ae44fc56aceef16687c0f0
  • Status changed from needs_work to positive_review

Thanks Julian. I tested all long again and it was fine.


New commits:

8ef768eMerge branch 'u/wuthrich/ticket/20254' of git://trac.sagemath.org/sage into ticket/20254
8b76743trac 20254: delete some comments and add doc

comment:11 Changed 4 years ago by vbraun

  • Status changed from positive_review to needs_work
$ git fetch trac /u/wuthrich/ticket/20254
fatal: Invalid refspec '/u/wuthrich/ticket/20254'

comment:12 Changed 4 years ago by wuthrich

  • Branch changed from /u/wuthrich/ticket/20254 to u/wuthrich/ticket/20254
git fetch trac u/wuthrich/ticket/20254

seems to work.

comment:13 Changed 4 years ago by wuthrich

  • Status changed from needs_work to positive_review

comment:14 Changed 4 years ago by wuthrich

Sorry if I did something wrong.

comment:15 Changed 4 years ago by vbraun

Thanks!

comment:16 Changed 4 years ago by vbraun

  • Status changed from positive_review to needs_work

Doctests fail (just as in the patchbot, click on the yellow questionmark in the ticket description)

comment:17 Changed 4 years ago by git

  • Commit changed from 8b7674311465d1a604ae44fc56aceef16687c0f0 to a13fdf4122ddb95f67d341dd3b9acad09d890d70

Branch pushed to git repo; I updated commit sha1. New commits:

a13fdf4trac 20254: one more doctest

comment:18 Changed 4 years ago by wuthrich

  • Status changed from needs_work to needs_review

Oi, I am sorry for overlooking this one. Not my day.

comment:19 Changed 4 years ago by saraedum

  • Status changed from needs_review to positive_review

comment:20 Changed 4 years ago by vbraun

Merge conflict with #14828

comment:21 Changed 4 years ago by vbraun

  • Status changed from positive_review to needs_work

comment:22 Changed 4 years ago by wuthrich

I can't work on this for a week at least. The resolution is that the file padic_lseries.py should be the one in this branch.

comment:23 Changed 4 years ago by git

  • Commit changed from a13fdf4122ddb95f67d341dd3b9acad09d890d70 to 8e53c1c85f28bd6ab10e3e2e998127b5ea8e9a67

Branch pushed to git repo; I updated commit sha1. New commits:

050bf73trac 20254: merge conflicts with 14828
8e53c1cMerge branch 'develop' into ticket/20254

comment:24 Changed 4 years ago by wuthrich

  • Status changed from needs_work to needs_review

comment:25 Changed 4 years ago by mmasdeu

  • Branch changed from u/wuthrich/ticket/20254 to u/mmasdeu/20254
  • Commit changed from 8e53c1c85f28bd6ab10e3e2e998127b5ea8e9a67 to f29d68508ffcaa40aadbfa1a6594633fdf388094

I have changed old style doctests ("...") in ell_modular_symbols.py to the new style ("....:"). This should turn the patchbot greener.

comment:26 Changed 4 years ago by saraedum

  • Status changed from needs_review to positive_review

comment:27 Changed 4 years ago by vbraun

  • Branch changed from u/mmasdeu/20254 to f29d68508ffcaa40aadbfa1a6594633fdf388094
  • Resolution set to fixed
  • Status changed from positive_review to closed
Note: See TracTickets for help on using tickets.