Speaker : Dr. Dr. Lalit Vaishya

Title of the Talk : Behavior of Hecke eigenvalues of automorphic form over certain sequences

Date, Time and venue : 24 March 2025, 12:00 PM - 1:00 PM at Seminar Hall, Dept of Mathematics.

Abstract : We present some of our work, which deals with some problems in number theory. In the first part of the talk, we present an analogue of the prime number theorem associated to binary quadratic forms with certain assumptions and its application.
In the second part of the talk, we consider a question concerning higher moments and behavior of signs of the Fourier coefficients of Hecke eigenforms indexed by a sparse set of integers. Moreover, we determine the size, in terms of conductor of associated L-function, for the first sign change of Hecke eigenvalues indexed by the integers, which are represented by a primitive integral positive-definite binary quadratic form of fixed discriminant $D<0$ with the class number $h(D) = 1$. In the third part of the talk, we present a result on the non-solvability of the Diophantine equation and the construction of a family of elliptic curves with
certain arithmetic properties.

At last, we aim to discuss our research proposal associated to Siegel modular forms, and asymptotic distribution on zeros of Jacobi form.

About the speaker : Dr. Lalit Vaishya is currently working as a DST-Inspire Faculty Fellow, at Stat-Math Unit, Indian Statistical Institute, New Delhi India. Prior to this he has done postdoctoral fellowships at the Institute of Mathematical Sciences, NISER Bhubaneswar and Kerala School of Mathematics. He has done Ph.D from Harish Chandra Research Institute, Prayagraj. His main research interests are Theory of Automorphic Forms and Analytic Number Theory.