A functional relation for Tornheim's double zeta functions

Tom 162 / 2014

Kazuhiro Onodera Acta Arithmetica 162 (2014), 337-354 MSC: Primary 11M32. DOI: 10.4064/aa162-4-2


We generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give new integral representations of several zeta functions, an extension of the parity result to the whole domain of convergence, concrete expressions of Tornheim's double zeta function at non-positive integers and some results on the behavior of a certain Witten's zeta function at each integer. As an appendix, we prove a functional equation for Euler's double zeta function.


  • Kazuhiro OnoderaDivision of Mathematics
    Chiba Institute of Technology
    Shibazono 2-1-1, Narashino
    Chiba 275-0023, Japan

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