Florin Boca : Correlations of Farey fractions and distribution of eigenvalues in large sieve matrices

Posted by Nathan Jones , part of the Number Theory Seminar.

At

March 4, 2022, 1 p.m.

In

Zoom

Abstract

The large sieve inequality provides an estimate for the largest eigenvalue of a matrix A*A, where A is a Vandermonde type rectangular matrix defined by the roots of unity of order at most Q. The talk will discuss some aspects concerning the behavior of the eigenvalues of these matrices when N ~ cQ^2, with Q large and c>0 constant. In particular, we are interested in asymptotic formulas for their moments, and in establishing the existence of a limiting distribution as a function of c. This is joint work with Maksym Radziwill.

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