#812: add Pollack/Stevens overconvergent modular symbols code
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Reporter: craigcitro | Owner: mmasdeu
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-feature
Component: modular forms | Resolution:
Keywords: p-adic | Merged in:
L-functions | Reviewers:
Authors: Marc Masdeu, | Work issues:
David Roe | Commit:
Report Upstream: N/A | fdedb5e340f2910df514de0ab32872070be3544c
Branch: u/mmasdeu/812 | Stopgaps:
Dependencies: |
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Comment (by mmasdeu):
All doctests pass now, finally! I have also checked for whitespace. There
are still things that one can work on, but my feeling is that they should
be relegated to other tickets depending on this one. Here is a list of
these:
1. The distributions code is embarrassingly slow. It would be drastically
improved by having an implementation that uses Sage's integers (no need to
use longs here) instead of Qp and Zp.
2. More functions/methods to interact with other implementations of
modular symbols could be added. For example, it is straightforward to have
a method to construct a Pollack-Stevens modular symbol from a one-
dimensional modular symbols space. Such a method exists if one starts from
an elliptic curve already.
3. The p-adic L-function returned by this implementation is quite
different to what is returned by the current (not overconvergent)
implementation. Fixing this involves deciding where the overconvergent
lift is done: one needs to know a target precision for this, whereas the
non-overconvergent implementation only requires the precision parameter
when evaluating a particular term of the series.
4. The normalization of the p-adic L-series is different than the one used
in the current implementation. This is noted in the examples, and it can
be easy to fix (once this ticket is accepted).
I am sure that there are many other improvements that other people will
suggest, but let's first ensure that this ticket doesn't see its 10th
birthday.
--
Ticket URL: <http://trac.sagemath.org/ticket/812#comment:41>
Sage <http://www.sagemath.org>
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