Fourier Interpolation with Zeros of Zeta and L-Functions

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