L-functions and modular forms

July 30 to August 3, 2007

at the

American Institute of Mathematics, Palo Alto, 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.