New strips of convergence for Dirichlet series

Abstract

Listen

Translate article

In this article we study the interplay of the theory of classical Dirichlet series in one complex variable with recent development on monomial expansions of holomorphic functions in infinitely many variables. For a given Dirichlet series we obtain new strips of convergence in the complex plane related to Bohr’s classical strips of uniform but non absolute convergence. absolute convergence of a Dirichlet series P ∞=1 a n ns on C. He made a deep connection with infinite dimensional holomorphy. His work is very much based on the fact that if p = (pk) ∞=1 is the sequence of prime numbers, then the sequence (log pk) ∞=1 is linearly independent over the field Q. Actually he associated to each series P ∞=1 a n ns a family of formal power series P α∈N (N) 0 apα pασ z α in infinitely many variables on the in