Ohio State is in the process of revising websites and program materials to accurately reflect compliance with the law. While this work occurs, language referencing protected class status or other activities prohibited by Ohio Senate Bill 1 may still appear in some places. However, all programs and activities are being administered in compliance with federal and state law.

Number Theory Seminar - Maksym Radziwill

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

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.

Events Filters: