Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier interpolation with zeros of zeta and $L$-functions   We construct a large family of Fourier interpolation bases for functions
analytic in a strip symmetric about the real line. Interesting examples involve
the nontrivial zeros of the Riemann zeta function and other $L$-functions. We
establish a duality principle for Fourier interpolation bases in terms of
certain kernels of general Dirichlet series with variable coefficients. Such
kernels admit meromorphic continuation, with poles at a sequence dual to the
sequence of frequencies of the Dirichlet series, and they satisfy a functional
equation. Our construction of concrete bases relies on a strengthening of
Knopp's abundance principle for Dirichlet series with functional equations and
a careful analysis of the associated Dirichlet series kernel, with coefficients
arising from certain modular integrals for the theta group.

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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: comp-gas