The Lerch Zeta Function II. Analytic Continuation

Details The Lerch Zeta Function II. Analytic Continuation The Lerch Zeta Function II. Analytic Continuation

2010-05-26

arxiv.org/abs/1005.4967v2

Mathematics

Number Theory

29 pages, 3 figures; v2 notation changes, homotopy action on left

Scientific paper

This is the second of four papers that study algebraic and analytic structures associated with the Lerch zeta function. In this paper we analytically continue it as a function of three complex variables. We that it is well defined as a multivalued function on the manifold M equal to C^3 with the hyperplanes corresponding to integer values of the two variables a and c removed. We show that it becomes single valued on the maximal abelian cover of M. We compute the monodromy functions describing the multivalued nature of this function on M, and determine various of their properties.

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