Number Theory Seminar - Maksym Radziwill

February 4, 2014
Monday, February 10, 2014 - 4:30pm to 5:30pm
MW 154
Maksym Radziwill

Title:  Some recent interactions between sieves and L-functions

SpeakerMaksym Radziwill, Institute of Advanced Study

Seminar Type:  Number Theory, Website

Abstract: I will discuss some recent work, where methods from sieve theory and L-functions interact. In the first direction, I will explain joint work with Kannan Soundararajan, where we find an "L-function analogue" of the Brun-Hooley sieve. Our method has several applications but I'll focus specifically on the problem of estimating small moments of L-functions. This particular problem has corollaries for the distribution of the Tate-Shafarevich group of primes twists of an elliptic curve or for the distribution of coefficients of half-integral weight modular forms.

Time permitting, I will also address the opposite direction, namely adapting technique from L-functions to problems of a more sieve theoretic character. In joint work with Kaisa Matomaki we use the idea of a mollifier, in a rather unusual context, to obtain sharp results on the number of sign changes of Fourier coefficients of Hecke eigencuspforms.

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