Asif Zaman

I will describe a version of the prime number theorem for arithmetic progressions that is uniform enough to deduce the Siegel-Walfisz theorem, Hoheisel's asymptotic for short intervals, a Brun-Titchmarsh bound and Linnik's bound for the least prime...

Abstract Quantum Unique Ergodicity has been a widely studied conjecture of Rudnick and Sarnak (1994), concerning the distribution of large frequency eigenstates on a negatively curved manifold. Arithmetic Quantum Unique Ergodicity (AQUE) restricts...

In 1944, Linnik famously showed unconditionally that the least prime in an arithmetic progression a (mod q) with gcd(a,q)=1 is bounded by q^L for some absolute effective constant L>0, known as “Linnik’s constant”. Many authors have computed explicit...