Analytic Continuations of Character and Alternating Tornheim Zeta Functions

Abstract

A method developed by Crandall is used to analytically continue character and alternating analogues of a double sum in three complex variables, known as the Tornheim or Mordell–Tornheim–Witten zeta function. We evaluate these functions at triples of nonpositive integer arguments in terms of generalized Bernoulli numbers, and determine those for which a given function is zero. Some special cases are related to tangent numbers.

Keywords:

• MSC: Primary 11M41

Additional information

Notes on contributors

Karl Dilcher

KARL DILCHER received his undergraduate education at the Technische Universität Clausthal in Germany. He then did his graduate studies at Queen’s University in Kingston, Ontario, and finished his Ph.D. there in 1983 under the supervision of Paulo Ribenboim. He is currently a professor at Dalhousie University in Halifax, Nova Scotia, Canada, where he first arrived in 1984 as a postdoctoral fellow. His research interests include classical analysis, special functions, and elementary and combinatorial number theory.

Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4R2

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