SAge Days 17 -- 3rd status reports
William Stein
== Friday September 18, 2009 ==
* Jared Weinstein: William and I proved if "so and so" then Heegner
class vanishes. Today: Actually write up proof.
* Amod Agashe: Checked my hunch that if an odd prime p divides a
Tamagawa number, but does not divide the order of the torsion
subgroup, then one can lower level by p for level up to 1010;
discussed my strategy for computing congruences with you and Randy;
discussed torsion and cuspidal subgroups with William and Soroosh. The
goal for Thursday was to get back safely, which was achieved!
* Tom Boothby: Robert Bradshaw and I played with power series
yesterday. Found great DiffEQ with easy solution. Unfortunately, we
left off a 1 in summing something, so we are now back to square one.
But we know exactly what $G_2$. Today: More of the same, but much
more careful.
* Robert Bradshaw: See Tom's status report. Got the database server
running. Today: Compute $G_2$. Textfile DB class.
* Sal Butt: I computed those integrals I was interested in, then
migrated C++ code to Sage; computing statistics on ap's; something is
going wrong. Today: Figure out what.
* Craig Citro: Playing with lambda internally. Eavesdropping on
Bradshaw and Boothby's conversation... and planned a hike. Computed
adjoint L-function one way, and doing another for consistency.
Today: Working through equations in a paper of Shimura to get
constants for functional equations. Finish create filter from lambda.
* Tim Dokchitser: General L-functions support; helped Amod figure out
answer to question about optimality for Amod. Massive help in quest
for $G_2$. Today: Is there a curve over Q(mu_7)^+ with everywhere
good reduction (or maybe bad at 7).
* Randy Heaton: (1) Automated more things I often do, e.g.,
index_in, eigendecomposition_of method. (2) Combine hints from
Craig, Victor, Hida, Shimura, Diamond-Shurman to get a nice formula
for Petersson for case of square-free level. Generalizing to
non-square-free level will be easy, but there is another
tricky-to-remove condition. Today: Learn trac. Go back to hotel,
then Florida safely.
* Robert Miller: Woke up early and drove Amod to ferry. Helping
Kevin S. with @parallel. Finished 2-descent. Needs review!! Today:
Randy trac, read about Heegner points, start refereeing William's
patch.
* Victor Miller: Flew home.
* Rishi: Writing program for L-functions associated to cusp forms.
Today: look at compact_system_of_eigenvalues.
* William Stein: Jared and I may have proved an interesting theorem
using "reciprocity"; Worked on Heegner points patch; conjectures with
Amod and Soroosh; PLAN: attack real component group problem, finish
Heegner points patch, put the rest of my databases into the new
database, and work on making an interface
* Kevin Steuve: working on prime_pi and nth-prime. improved my code
style. all functionality in a single python class. Benchmarking
prime_pi, and comparing using sieving to calling is_prime on interval;
found under some conditions it if faster to use primality tests.
Comparing is_prime versus is_pseudoprime. Today: prime_pi is fast
and nth prime; Going to optimize nth prime and make a sparse cache.
* Soroosh Yazdani: Looking at Amod's conjectures... true or no hope?
Paper of Tang -- reading this; nice proof. Modular symbols mod 2.
TODAY: Play around with component group more today.
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org