香蕉视频

Title: A new approach to zero-free regions.

Abstract: The method of de la Vall茅e Poussin establishes the classical zero-free region for the Riemann zeta function. It has been generalized to establish zero-free regions for all automorphic L-functions, as well as many GL(m)xGL(n) Rankin-Selberg L-functions. However, for a typical Rankin-Selberg L-function, we do not yet know how to execute the method of de la Vall茅e Poussin, and only very weak (but still nontrivial) zero-free regions are available. I will talk about a new method for establishing zero-free regions for L-functions. This new method leads to the strongest t-aspect zero-free region for general GL(m)xGL(n) Rankin-Selberg L-functions, considerably improving on earlier work. This leads to a substantial improvement in the error term in the prime number theorem for such L-functions. I will describe ongoing work with Gergely Harcos.The method of de la Vall茅e Poussin establishes the classical zero-free region for the Riemann zeta function. It has been generalized to establish zero-free regions for all automorphic L-functions, as well as many GL(m)xGL(n) Rankin-Selberg L-functions. However, for a typical Rankin-Selberg L-function, we do not yet know how to execute the method of de la Vall茅e Poussin, and only very weak (but still nontrivial) zero-free regions are available. I will talk about a new method for establishing zero-free regions for L-functions. This new method leads to the strongest t-aspect zero-free region for general GL(m)xGL(n) Rankin-Selberg L-functions, considerably improving on earlier work. This leads to a substantial improvement in the error term in the prime number theorem for such L-functions. I will describe ongoing work with Gergely Harcos.

Venue: Concordia University, Library Building, 9th floor, room LB 921-4