Mathematical Sciences

Title :

Distributions of hypergeometric functions over finite fields

Area of research :

Mathematical Sciences

Focus area :

Arithmetic Statistics

Principal Investigator :

Ms. Neelam Saikia, Assistant Professor, Indian Institute of Technology (IIT), Bhubaneswar

Timeline Start Year :


Contact info :


Executive Summary :

Arithmetic statistics is an active area of number theory, focusing on distributional results for fundamental objects. The Sato-Tate conjecture, formulated by mathematicians Sato and Tate in the 1960s, is celebrated for its semicircular distribution. This project aims to investigate distributional results for hypergeometric functions over large finite fields, focusing on new distributions for certain families of Greene's hypergeometric functions. Methods include harmonic mass forms, modular forms, class numbers, and elliptic curves.

Organizations involved