PROJECT GROUPS

Contents

Computing the Cartier operator acting on 1-forms

PEOPLE: Rachel P., Aly, Gagan, Anja, Sarah, Marina, Kate

See this page.
sage worksheet that is slow and just implements algorithm (correctly!)
- - this appears to be done here: Computing N for Hyperelliptic curve.sws - need data to check that this is correct.
make it really, really fast.
get included in sage itself
make a big table or something? Rachel: "I would love to find a curve with p-rank 0 and a-number 1. I did genus 4 and p=3."

PEOPLE: Kate, William S., Lola, Aly, Erin, Bianca

smalljac
- make smalljac code usable from Python (involves Cython); see this psage issue.
- use code:
  - - replicate and extend data in Kate's talk - maybe try genus 2 analogue?
cubic and sextic residue symbol
- there's a ticket that has only partial implementation (cubic residue of rational prime and element of Q(sqrt(-3))) -- not at all a general implementation
- there are artin symbols etc. -- big machinery
- we think a fast independent implementation of the cubic (and sextic) residue symbol is worthwhile
- what does SAGE do to compute quadratic residue symbols?
explicit calculation of Grossencharacters (aka Hecke characters).

PEOPLE: Jennifer B., Jennifer P., Jennifer J.

Decide if curve is attached to a modular form, and if so find it, then use that to compute L-series.
Plug L-series into Dokchitser and get numbers.
Make a table. Starting with "van Wamelen"'s table. See also Kohel's tables.
Incorporate Robert Bradshaw's code into Purple Sage. http://code.google.com/p/purplesage/issues/detail?id=14

PEOPLE: William S., Bianca,

Make a list of what you want to be able to do:
- - Such computations come up for Stein in http://wstein.org/papers/kolyconj2/
List why Magma/PARI aren't good enough (bugs, issues, speed, etc.)
Write really really fast code to implement some of this.

PEOPLE: Needs people!