Title: Estimates for the zeros of Riemann zeta-function via Fourier analysis
Speaker: Micah Milinovich, University of Mississippi
Seminar Type: Number Theory Seminar
Abstract: In this talk I will show how to use certain Beurling-Selberg type majorants and minorants of exponential type in conjunction with the Guinand-Weil explicit formula to study the vertical distribution of the zeros of the Riemann zeta-function. We can use these techniques to prove the sharpest known bounds for the number zeros in a long interval on the critical line (assuming the Riemann hypothesis) and also to study local statistics of zeros (i.e. pair correlation). Our results on pair correlation extend earlier work of P. X. Gallagher and give some evidence for the famous conjecture of H. L. Montgomery. This is based on joint works with Emanuel Carneiro, Vorrapan Chandee, and Friedrich Littmann.
