Some Extremal Functions in Fourier Analysis and Applications to Number Theory

SHORT TALKS BY POSTDOCTORAL MEMBERS
Topic:Some Extremal Functions in Fourier Analysis and Applications to Number Theory
Speaker:Emanuel Carneiro
Affiliation:Member, School of Mathematics
Date:Tuesday, September 22
Time/Room:4:00pm - 5:00pm/S-101

I will give an overview on the recent developments on the Beurling-Selberg problem of majorization by entire functions of exponential type, in joint works with J.D. Vaaler (Texas) and F. Littmann (North Dakota State). These provide new applications to number theory that include: Hilbert-type inequalities, Erdos-Turan-type inequalities and, more recently, bounds for the Riemann zeta function on the critical line (work of Chandee-Soundararajan).