The weak Gram law for Hecke $$ L $$-functions

Abstract

AbstractWe generalize a theorem by Titchmarsh about the mean value of Hardy’s $$Z$$ Z -function at the Gram points to the Hecke $$L$$ L -functions, which in turn implies the weak Gram law for them. Instead of proceeding analogously to Titchmarsh with an approximate functional equation we employ a different method using contour integration.