Number Theory Seminar
Florin Boca
University of Illinois at Urbana-Champaign
Correlations of Farey fractions and distribution of eigenvalues in large sieve matrices
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.
Join Zoom Meeting
https://uic.zoom.us/j/88173268700?pwd=aEhmTGpSOVhidWE4L1VWUnNhNVlvUT09
Meeting ID: 881 7326 8700
Passcode: 0t198j41
Friday March 4, 2022 at 1:00 PM in Zoom