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Complex B-splines and Hurwitz zeta functions

Part of: Zeta and $L$-functions: analytic theory Numerical approximation and computational geometry

Published online by Cambridge University Press:  10 April 2013

B. Forster ,
R. Garunkštis ,
P. Massopust  and
J. Steuding
B. Forster
Affiliation:
Fakultät für Informatik und Mathematik,Universität Passau,Innstr. 33, 94032 Passau,Germany email brigitte.forster@uni-passau.de Institut für Biomathematik und Biometrie,Helmholtz Zentrum München,Ingolstädter Landstraße 1,85764 Neuherberg,Germany email brigitte.forster@uni-passau.demassopust@ma.tum.de
R. Garunkštis
Affiliation:
Faculty of Mathematics and Informatics,Vilnius University,Naugarduko 24, 03225 Vilnius,Lithuania email ramunas.garunkstis@mif.vu.lt
P. Massopust
Affiliation:
Institut für Biomathematik und Biometrie,Helmholtz Zentrum München,Ingolstädter Landstraße 1,85764 Neuherberg,Germany email brigitte.forster@uni-passau.demassopust@ma.tum.de Zentrum Mathematik, M6,Technische Universität München,Boltzmannstr. 3, 85747 Garching,Germany email massopust@ma.tum.de
J. Steuding
Affiliation:
Department of Mathematics,Würzburg University,Am Hubland, 97074 Würzburg,Germany email steuding@mathematik.uni-wuerzburg.de

Abstract

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We characterize nonempty open subsets of the complex plane where the sum $\zeta (s, \alpha )+ {e}^{\pm i\pi s} \hspace{0.167em} \zeta (s, 1- \alpha )$ of Hurwitz zeta functions has no zeros in $s$ for all $0\leq \alpha \leq 1$. This problem is motivated by the construction of fundamental cardinal splines of complex order $s$.

MSC classification

Secondary: 11M35: Hurwitz and Lerch zeta functions 65D07: Splines 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses 65D05: Interpolation
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 16 , October 2013 , pp. 61 - 77
Copyright
© The Author(s) 2013 

References

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