The Okada space and vanishing of ${L(1,{f})}$

Murty, M. Ram; Pathak, Siddhi

doi:10.7169/facm/1952

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Proof Of Theorem 3 and A Counterexample By Tengely1

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2022

2023

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Cited by 2 publications

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“…In [22,Theorem 4.8], the authors proved the following : Suppose N ≡ 2 mod 4 and the function f is of period N taking values in {±1}. Then L(1, f ) = 0 whenever the infinite sum converges.…”

Section: Proof Of Theorem 3 and A Counterexample By Tengelymentioning

confidence: 99%

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On Primitivity and Vanishing of Dirichlet Series

Bharadwaj¹

2022

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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 Erdös holds. We also characterize rational valued periodic functions for which the associated Dirichlet series vanishes at two different positive integers under some additional conditions.

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Section: Proof Of Theorem 3 and A Counterexample By Tengelymentioning

confidence: 99%

“…Vanishing when the period is even : When N is even, we can construct examples of functions f with values in {±1} of period N for which Property U does not hold. This section is partially motivated by the works [22], [27] and [19].…”

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confidence: 99%