A conjecture of S. Chowla via the generalized Riemann hypothesis

Abstract

S. Chowla conjectured that if p = m 2 + 1 p = {m^2} + 1 is prime and m > 26 m > 26 , then h K {h_K} , the class number of K = Q ( p ) K = Q(\sqrt p ) , is greater than 1. We prove this conjecture under the assumption of the Riemann hypothesis for ς K \varsigma K , the zeta function of K K , i.e. the generalized Riemann hypothesis (GRH).