Classical Hermite and Laguerre Polynomials and the zero-distribution of Riemann's ζ-function

Abstract

Necessary and sufficient conditions for absence of zeros of the function ζ(s), s=σ+it, in the half-plane σ>θ, 1/2≤θ<1 are proposed in terms of representations of holomorphic functions by series in Hermite and Laguerre polynomials as well as in terms of Fourier and Hankel integral transforms. 2010 Mathematics Subject Classification: 11M26, 33C45, 42A38.