Modified L-functions
Articles
Eugenijus Stankus
Vilnius University
Published 2008-12-21
https://doi.org/10.15388/LMR.2008.07
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Keywords

analyticity
generalized number
L-function
residue
zeta-function

How to Cite

Stankus, E. (2008) “Modified L-functions”, Lietuvos matematikos rinkinys, 48(proc. LMS), pp. 44–47. doi:10.15388/LMR.2008.07.

Abstract

The sequence of generalized prime numbers q0 = 1, qn = pkn+1 -1, n N, and the corresponding zeta-function Zk(s) = \prodp>2( 1 - (pk - 1)-s)-1 , s = σ + it, are analyzed. The analyticity of Zk(s) in the domain σ > 0, except for a simple pole s = 1/k , is proved.

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