#
L-functions and modular forms

July 30 to August 3, 2007
at the

American Institute of Mathematics,
San Jose, California

organized by

Kiran Kedlaya,
Michael Rubinstein,
Nathan Ryan,
Nils-Peter Skoruppa,
and William Stein

## Original Announcement

This workshop will initiate a major new project to
gather and organize data and methods for understanding and
computing with L-functions and modular forms. The goal is to
produce extremely easy to use and well documented databases
and software for use by researchers and students.
At the workshop, participants will organize the project, and begin
work on specific details. Our goal is that by the end of the workshop we
will have a first usable prototype that will provide a template for
additional work by participants after the workshop.
This ambitious project will require help: organization of an encyclopedia, creation
of a list of problems to focus and orchestrate our work, implemention of algorithms,
construction of databases, and finding solutions to engineering aspects of creating
and managing a very easy-to-use and well-documented database.

L-functions are categorized in the first place by degree. The degree one
L-functions are the Riemann zeta function and Dirichlet L-functions.
Degree two L-functions conjecturally all arise from primitive, cuspidal
modular forms, both the holomorphic and non-holomorphic (Maass) forms.
For degree higher than two, examples include convolutions of degree two
L-functions; there are specific examples of higher degree L-functions that
do not arise in this way, for example Siegel modular forms that are not lifts.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.