On Fourier and Zeta(s)

Abstract

We study some of the interactions between the Fourier Transform and the Riemann zeta function (and Dirichlet-Dedekind-Hecke-Tate L-functions)

50 pages. Oct 2002: Final ms, to appear in Forum Mathematicum. March 2003: we have become aware that Duffin and Weinberger had discovered earlier the ``co-Poisson formula''. See added footnote on page 3. Our whole analysis, and especially the connections with the zeta function, remains a novel contribution

References in corpus (2)

• A strengthening of the Nyman-Beurling criterion for the Riemann Hypothesis
• Sur les Formules Explicites I: analyse invariante

Cited by in corpus (10)

• On a representation of the idele class group related to primes and zeros of L-functions
• H = x p with interaction and the Riemann zeros
• Rigorous quantum field theory functional integrals over the p-adics I: anomalous dimensions
• The Lerch Zeta Function I. Zeta Integrals
• The Lerch zeta function IV. Hecke operators
• Scattering, determinants, hyperfunctions in relation to Gamma(1-s)/Gamma(s)
• Deux extensions de Théorèmes de Hamburger
• The Riemann zeta in terms of the dilogarithm
• The Lerch zeta function and the Heisenberg group
• Two complete and minimal systems associated with the zeros of the Riemann zeta function