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Derivatives and Special Values of Higher-Order Tornheim Zeta Functions

dc.contributor.authorDilcher, Karl
dc.contributor.authorTomkins, Hayley
dc.date.accessioned2019-01-02T15:37:40Z
dc.date.available2019-01-02T15:37:40Z
dc.date.issued2018
dc.description.abstractWe study analytic properties of the higher-order Tornheim zeta function, defined by a certain $n$-fold series ($n\geq 2$) in $n+1$ complex variables. In particular, we consider the function $\omega_{n+1}(s)$, obtained by setting all variables equal to $s$. Using a free-parameter method due to Crandall, we first give an alternative proof of the trivial zeros of $\omega_{n+1}(s)$ and evaluate $\omega_{n+1}(0)$. Our main result, however, is the evaluation of $\omega_{n+1}'(0)$ for any $n\geq 2$. This is again achieved by using Crandall's method, and it generalizes recent results in the cases $n=2, 3$. Properties of Bernoulli numbers and of higher-order Bernoulli numbers and polynomials play an important role throughout this paper.en_US
dc.identifier.urihttp://hdl.handle.net/10222/75063
dc.titleDerivatives and Special Values of Higher-Order Tornheim Zeta Functionsen_US
dc.typePreprinten_US

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