Number Theory Seminar
Speaker: Arshay Seth, School of Mathematics, TIFR
Host: Ravi Raghunathan
Title: Euler products inside the critical strip
Time, day and date: 11:30:00 AM – 12:30:00 PM, Tuesday, October 27
Venue: Room 113
Abstract: Even though Euler products of L-functions are generally valid only to the right of the critical strip, there is a strong sense in which they should persist even inside the critical strip.  Indeed, the behaviour of Euler products inside the critical strip is very closely related to both the Riemann Hypothesis and the Birch and Swinnerton-Dyer conjecture.  In this talk, we will give an introduction to this topic and then discuss recent work on establishing asymptotics for partial Euler products of L-functions in the critical strip.  We will end by giving applications of these results to questions related to Chebyshev's bias, and also discuss a new conjectural local-global principle for higher genus curves. This talk is partly based on joint works with Alina Bucur, Kiran Kedlaya and Shin-ya Koyama.