Seminario de Teoría de Números

Variants of Lehmer’s Conjecture for Ramanujan’s tau-function

SPEAKER: Ken Ono (University of Virginia)

DATE & TIME: Jueves 08 de mayo - 16:30

VENUE: Aula 520, Departamento de Matemáticas, UAM.

ABSTRACT:  

Modular forms are generating functions ofimportant  
quantities in arithmetic geometry, combinatorics, number theory, and  
physics. Despite many deep developments in the arithmetic geometric  
and analytic aspects (e.g. Deligne's proof of the Weil Conjectures,  
the development of Galois representations, Birch and Swinnerton-Dyer  
Conjecture, to name a few), some of the seminal questions about them  
remain open. Perhaps the most prominent of these is Lehmer's  
Conjecture on the nonvanishing of modular form coefficients such as  
Ramanujan's tau-function. In joint work with J. Balakrishnan, W.  
Craig, and W.-L. Tsai, the speaker has obtained the first results that  
establish that many integers are never modular form coefficients.