Fourier Interpolation with Zeros of Zeta and L-Functions
Peer reviewed, Journal article
Published version
Permanent lenke
https://hdl.handle.net/11250/3051860Utgivelsesdato
2022Metadata
Vis full innførselSamlinger
- Institutt for matematiske fag [2531]
- Publikasjoner fra CRIStin - NTNU [38672]
Sammendrag
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.