A functional relation for Tornheim's double zeta functions

• Autorzy: Kazuhiro Onodera
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11M32: Multiple Dirichlet series and zeta functions and multizeta values

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 162
• Numer: 4
• Strony: 337-354

Daty

wydano

2014

Twórcy

autor

Kazuhiro Onodera

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

Identyfikatory

DOI

10.4064/aa162-4-2