Sign changes of coefficients of certain Dirichlet series

Abstract

Abstract. In this paper, we give criteria for infinitely many sign changes of the coefficients of any Dirichlet series if the coefficients are real numbers. We also provide examples where our criteria are applicable.

Sign changes of coefficients and sums of coefficients of L-functions

“…Indeed, they achieve this later in [24] in the case of real coefficients of L-functions of automorphic irreducible self-dual cuspidal representations of GL 2 (A Q ). In another work by Meher and others [25], sign change results are obtained immediately from the analytic properties of automorphic L-functions.In Section 2 of this paper, we extend the Meher-Murty axiomatization guaranteeing quantitative results on sign changes to sequences of complex coefficients. We also present a new axiomatization that gives intervals of sign changes directly from the growth of associated L-functions on vertical strips.…”

“…Indeed, they achieve this later in [24] in the case of real coefficients of L-functions of automorphic irreducible self-dual cuspidal representations of GL 2 (A Q ). In another work by Meher and others [25], sign change results are obtained immediately from the analytic properties of automorphic L-functions.…”