TAGG seminar

Abstract: One of the major achievements of the spectral theory of automorphic forms is the study of primes in arithmetic progressions with moduli beyond the square-root barrier on average. The price for these results, however, is a restriction to weights with favorable factorization properties. In upcoming joint work with J. Merikoski and J. Duker-Lichtman, we obtain new results interpolating between the classical Bombieri–Vinogradov range and automorphic methods. Our approach is based on a new perspective on spectral techniques that circumvents the use of Kloosterman sums and the technical restrictions they impose.