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Complex B-splines and Hurwitz zeta functions
Published online by Cambridge University Press: 10 April 2013
Abstract
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 $s$.
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- © The Author(s) 2013
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