A functional relation for Tornheim's double zeta functions

Kazuhiro Onodera. "A functional relation for Tornheim's double zeta functions." Acta Arithmetica 162.4 (2014): 337-354. <http://eudml.org/doc/279526>.

@article{KazuhiroOnodera2014,
abstract = {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.},
author = {Kazuhiro Onodera},
journal = {Acta Arithmetica},
keywords = {double zeta function; Witten zeta function; double zeta values; functional equation},
language = {eng},
number = {4},
pages = {337-354},
title = {A functional relation for Tornheim's double zeta functions},
url = {http://eudml.org/doc/279526},
volume = {162},
year = {2014},
}

TY - JOUR
AU - Kazuhiro Onodera
TI - A functional relation for Tornheim's double zeta functions
JO - Acta Arithmetica
PY - 2014
VL - 162
IS - 4
SP - 337
EP - 354
AB - 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.
LA - eng
KW - double zeta function; Witten zeta function; double zeta values; functional equation
UR - http://eudml.org/doc/279526
ER -