== Wed September 16, 2009 ==
* Amod Agashe: did: arrived safely; testing level lower conjecture
when no p-torsion up to level 800. plan to do: run code further;
investigate Soroosh counterexample at 13; way to capture congruences
only with old forms; craig and congruences with old forms.
* Tom Boothby: did: nearly finished disk caching and parellelizing
decorator; plan to do: math -- million digits of Sha?
* Robert Bradshaw: did: dokchitser for computing L-functions. figured
out problem, but found others; plan to do: millions digits of Sha.
* Sal Butt: did: worked through kedlaya-sutherland about statistics
of L-polynomials (Euler factors at places of good reduction? over QQ.
"the symplectic group") and now taking their ideas to do what I want
to do. I'm doing this in the function field case. Now I'm looking at
L-polynomial in function field case and doing analogue. Written sage
code, but there are bugs. plan to do: debug and do calculation.
* Craig Citro: creates inputs to Dokchitser algorithm for a bunch of
L-function; plan to do: continue
* Tim Dokchitser: helped Robert figure out precision issue; talk to
people. plan to do: look at Amod's conjecture.
* Randy Heaton: wrote two small patches to automize stuff I do a lot
with modular forms. worked out almost everything to compute petersson
inner product. Need: (1) prove small result, (2) talk to Robert and
Craig about computing L-functions, (3) talk to Craig about a level
raising constant relating Petersson of old form and new form -- what
is the Petersson norm of an image. plan to do: the above, plus todos
in the source code, plus newforms don't no they're newforms.
* Robert Miller: got mom to airport and got a cable for TV!; plan to
do: binary codes into database, working on descent, or anything else.
* Victor Miller: tearing hair out looking at paper of Yang, and got
some of it implemented. Yang defines a bunch of modular functions
with character on Gamma(N) with divisors supported on the cusps. He
gets generators by taking products that kill action of character. He
makes claims about them generating... but then he uses only a much
simpler class of functions. I'm implementing both. Question: is
there support for Puiseaux series. I noticed also that power series
over cyclotomic fields: $x^10000$ takes forever; making it takes
forever. Plan to do: Implement other class of functions; lattice
reduction to find good multiplicative basis. (The more I read this
paper, the more I am annoyed!) Get the nitty gritty of classes in
Sage right. This is all a generalization of David Loeffler's eta
products code.
* Rishi: Did everything Cremona suggested in his review, except
Cremona's class hierarchy is impossible. Implemented a Dirichlet
L-function. Today: Given a newform find the corresponding L-series
that does everything Rubinstein's library provides.
* William Stein: Heegner points (explained to Jared and came up with
a fascinating conjecture plus a great consistency check), real
component group (compute action of Atkin-Lehner and Hecke), cuspidal
torsion (lots of conjectures, counterexamples). Today: try to prove
real component group conjecture by following Ling-Oesterle's result on
Shimura subgroup. Make and organize more modular forms tables.
* Kevin Steuve: Compressing tables of differences between Li(x) and
pi(x) by looking at differences of errors. Using lza only save 1/8 th
disk space (thought we would get more). Also made my code use
multi-core above $10^{12}$. Today: working on $n$th prime function
using Victor Miller's linear interpolation method.
* Jared Weinstein: As William said, we identify pattern in vanishing
of Kolyvagin classes associated to elliptic curve of rank 2. We found
conjecture that predicts a sufficient condition for them to vanish.
TODO: Want to find a necessary condition for vanishing.
* Soroosh Yazdani: Look at cuspidal torsion, and ideas for proving
it. Discussed example of multiplicity one failing for Eisenstein
primes. Trying to understand action of Atkin-Lehner on real
components of J0(N) (an F2 vector space). When there are three prime
divisor of N, there is a basis such that action is straightforward,
but for 4 primes not clear. Also, full Atkin-Lehner involution acts
trivially on component group. Today: But Amod has other ideas about
extending Mazur.
Meeting about making online tables at 2:30 clock to discuss modular
forms database.
Somebody: Implement Shimura subgroup
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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