CANCELLED: L-functions in Analytic Number Theory: Sneha Chaubey

The topic on the distribution of sequences saw its light with the seminal paper of Weyl. While the classical notion of equidistribution modulo one addresses the “global” behaviour of the fractional parts of a sequence, quantities such as k-point correlations and nearest neighbour gap distributions are useful in investigating the sequence on finer scales. In this talk, we discuss these fine-scale statistics for real-valued arithmetic sequences, and show that the limiting distribution of the nearest neighbour gaps of real-valued lacunary sequences is Poissonian. We also prove the Poissonian behavior of the 2-point correlation function for certain classes of real-valued vector sequences. This is achieved by extrapolating conditions on the number of solutions of Diophantine inequalities using twisted moments of the Riemann zeta function.