Projects

Analytic Number Theory

Guide - Dr. Sneha Chaubey

I studied the proofs of prime number theorem, Siegel‐Walfisz theorem, and Bombieri‐Vinogradov theorem. I mainly followed the texts of “Multiplicative Number Theory” by Davenport, Montgomery‐Vaughan and “The Distribution of Prime Numbers” by Dimitris Koukoulopoulos.

p-adic Number Theory

Guide - Dr. Anup Dixit

I studied chapters 1, 2, and 4 from Neal Koblitz’s “p‐adic Numbers, p‐adic Analysis and Zeta functions”. I read the following papers as part of the project: “The derivative of p‐adic Dirichlet series at s=0” [Stark’s Conjectures: Recent Work and New Directions, (2004)] and “On the p‐adic series involving the infinite sum n^{k}. n! [CRM Lecture Notes, 2004]. I could generalize the results of the second paper for arithmetic progressions.