American Institute of Mathematics, Palo Alto, California
Kiran Kedlaya, Michael Rubinstein, Nathan Ryan, Nils-Peter Skoruppa, and William Stein
This workshop, sponsored by AIM and the NSF, 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.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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