Title of the talk: " The pair correlation statistic in number theory and Fourier optimization"

Date & Time: 31 Oct. 2025  at 05:00 PM

Abstract: In this seminar, we will discuss the pair correlation statistic for number-theoretic sequences. We briefly describe the uniform distribution and Possonian pair correlation. Then, we discuss our current work related to GUE pair correlation statistic: consider analogs of Montgomery’s form factor for zeros of the Riemann zeta function in the case of arbitrary sequences satisfying some basic assumptions and connect their estimation to two extremal problems in Fourier analysis, which are promptly studied. As applications, we provide average bounds of form factors related to some sequences of number theoretic interest, such as the zeros of primitive elements of the Selberg class, Dedekind zeta functions, and the real and imaginary parts of the Riemann zeta function. In the last case, our results bear an implication to a conjecture of Gonek and Ki (2018), showing it cannot hold in some situations. This is joint work with T. Ismoilov and A. P. Ramos from SISSA, Trieste.

About the Speaker: Dr. Mithun is currently a Postdoctoral fellow at the International Centre for Theoretical Physics-ICTP, Italy. He is also an Inspire Faculty Fellow at NISER-Bhubaneswar. Prior to this he was a Post-doctoral fellow at IMSc-Chennai (November 2021-September 2022). Before he was a Postdoctoral fellow at IISER-Berhampur.(January-October, 2021). He was at ISI-Kolkata as a visiting scientist (February-December, 2020). He completed my PhD form Harish-Chandra Research Institute, Prayagraj on January 2021. His research interest lie in Number theory (probabilistic, analytic) and Harmonic analysis.