#812: add Pollack/Stevens overconvergent modular symbols code
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Reporter: craigcitro | Owner: craigcitro
Type: enhancement | Status: new
Priority: major | Milestone: sage-feature
Component: modular forms | Keywords: p-adic L-functions
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Changes (by was):
* upstream: => N/A
Comment:
From Jennifer Balakrishnan:
Rob Pollack just ported over some of his p-adic L-series via
overconvergent modular symbols code to Sage, which could be very
useful for our p-adic BSD paper.
The code he sent me originally didn't quite produce results matching
our data, but I've worked on it over the last few days, fixed a few
bugs, noticed a few more, and thought this might be a good coding
sprint project for us this week.
Here's where the code currently stands:
-- it can compute the p-adic L-series in the split p case (with data
matching what we've already computed naively)
-- Rob says inert p is straightforward, just a matter of knowing how
to call the right objects in Sage, which I think I can do
-- I've tested it against the regulators I computed in my thesis, and
we can easily produce 10+ digits of precision in the L-value!!
-- for some primes, it results in memory errors (I've put examples,
working and not, in the docstring in the test file). I'm not sure how
to fix these.
As an enhancement, maybe we could also use some of your very fast code
for modular symbols?
Perhaps most mathematically interesting, the special values computed
by his program also result in the same +/-1 "sign" in the BSD formula
that our previous methods produced!
The code is available here:
http://sage.math.washington.edu/home/jen/OMS
To run it, attach master.sage and Jen/test_run_generic.sage. The
second file
(http://sage.math.washington.edu/home/jen/OMS/Jen/test_run_generic.sage)
has some examples in the docstring.
Jen
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/812#comment:6>
Sage <http://www.sagemath.org>
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