# Fourier Interpolation with Zeros of Zeta and L-Functions

```@article{Bondarenko2022FourierIW,
title={Fourier Interpolation with Zeros of Zeta and L-Functions},
author={Andriy V. Bondarenko and Danylo V. Radchenko and Kristian Seip},
journal={Constructive Approximation},
year={2022}
}```
• Published 6 May 2020
• Mathematics
• Constructive Approximation
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…
2 Citations

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• A. Kulikov
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We prove that under very mild conditions for any interpolation formula f(x)=∑λ∈Λf(λ)aλ(x)+∑μ∈Mf^(μ)bμ(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}

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We prove that under very mild conditions for any interpolation formula f(x)=∑λ∈Λf(λ)aλ(x)+∑μ∈Mf^(μ)bμ(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}

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