L-functions, sieves and the Tate Shafarevich group

Special Number Theory Seminar
Topic:L-functions, sieves and the Tate Shafarevich group
Speaker:Maksym Radziwill
Affiliation:Member, School of Mathematics
Date:Tuesday, April 8
Time/Room:3:30pm - 4:30pm/Fine 1201, Princeton University

I will explain joint work with Kannan Soundararajan, where we find an "L-function analogue" of the Brun-Hooley sieve. Essentially, our method allows us to work analytically with long truncated Euler products inside the critical strip. As a consequence we obtain several new results on the distribution of the central values of families of L-functions. In particular I'll focus on consequences for the distribution of the Tate-Shafarevich group of (prime) twists of an elliptic curve.