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On Primitivity and Vanishing of Dirichlet Series by Bharadwaj, Abhishek is a scholarly article available to read on EtoBox.

What is On Primitivity and Vanishing of Dirichlet Series about?

For a rational valued periodic function, we associate a Dirichlet series and provide a new necessary and sufficient condition for the vanishing of this Dirichlet series specialized at positive integers. This question was initiated by Chowla, and carried out by Okada for a particular infinite sum. Our approach relies on the decomposition of the Dirichlet characters in terms of primitive characters. Using this, we find some new family of natural numbers for which a conjecture of Erd\"os holds. We also characterize rational valued periodic functions for which the associated Dirichlet series vanishes at two different positive integers under some additional conditions.

Author

Bharadwaj, Abhishek

Published

2022

Language

EN