The critical values of certain dirichlet series

Abstract

We investigate the values of several types of Dirichlet series D(s) for certain integer values of s, and give explicit formulas for the value D(s) in many cases. The easiest types of D are Dirichlet L-functions and their variations; a somewhat more complex case involves elliptic functions. There is one new type that includes Σn=1∞(n2 + l)-s for which such values have not been studied previously.