Modified L-functions - Stankus, Eugenijus (Lietuvos matematikos rinkinys, 2008)
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.
Keywords: analyticity; generalized number; L-function; residue; zeta-function