L-functions, sieves and the Tate Shafarevich group

L-functions, sieves and the Tate Shafarevich group

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Maksym Radziwill , IAS
Fine Hall 1201

Please note special day, time and location.   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.