Sum of the Hurwitz-Lerch Zeta Function over Prime Numbers: Derivation and Evaluation

Robert Reynolds; Allan Stauffer

Sum of the Hurwitz-Lerch Zeta Function over Prime Numbers: Derivation and Evaluation

General Mathematics 2022-04-11 v1

Authors: Robert Reynolds , Allan Stauffer

Abstract

For the function $f(m,p,q,n)$ , where $k,s,a$ general complex numbers and $q$ any positive integer, we establish the sum of values of the Hurwitz-Lerch zeta function $\Phi(f(m,p,q,n),k,a)$ taken at prime numbers $n$ . Special cases of this sum are evaluated in terms of products of trigonometric functions and Catalan's constant $K$ .

Keywords

Hurwitz-Lerch zeta function prime numbers summation Catalan's constant trigonometric functions evaluation

Cite

@article{arxiv.2204.03821,
  title  = {Sum of the Hurwitz-Lerch Zeta Function over Prime Numbers: Derivation and Evaluation},
  author = {Robert Reynolds and Allan Stauffer},
  journal= {arXiv preprint arXiv:2204.03821},
  year   = {2022}
}

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