Alladi Ramakrishnan Hall

On analogues of the Brun-Titchmarsh theorem and some applications

Jyothsnaa Sivaraman

ISI Bangalore

Dirichlet's theorem on primes in arithmetic progressions states that for any two integers a,q with gcd(a, q) =1 there are infinitely many primes p \equiv a mod q. An asymptotic for the number of such primes was provided by de la Vallee Poussin. But in terms of fully explicit bounds the best known upper bound is given by the Brun-Titchmarsh theorem. In this talk, we discuss two generalisations of the Brun-Titchmarsh theorem and some of their applications. This is the subject of joint work with Prof. Sanoli Gun and Prof. Olivier Ramare.