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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-4-2,
author = {Kazuhiro Onodera},
title = {A functional relation for Tornheim's double zeta functions},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {337-354},
zbl = {1292.11096},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-4-2}
}
Kazuhiro Onodera. A functional relation for Tornheim's double zeta functions. Acta Arithmetica, Tome 166 (2014) pp. 337-354. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-4-2/