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

descriptionPublicationkeyboard_double_arrow_right Preprint 07 Apr 2022Funded by:NSERC | unidentified
Authors: Reynolds, Robert; Stauffer, Allan;

arXiv: 2204.03821

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

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

30E20, 33-01, 33-03, 33-04, Mathematics - General Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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