there is a representation of the Zeta function as Mellin transform of the fractional part function. The idea of B.Nyman was about a proper translation of the RH into properties of this fractional part function. This criterion can be formulated in a purely Functional Analysis Hilbert space framework (B. Bagchi) using weighted l2-spaces defined by the fractional part function with argument (k/n). The note below contains two parts: - a Zeta fake representation as Mellin transform of the Hilbert-transformed fractional part function, which has all its zero on the critical line and is identical to the Zeta function in a weak sense. This gives a 2nd - a proposal to move from a Fourier- to a
The note above was motivated by this paper
Main results concerning Lommel polynomials are recalled from the papers:
Papers from the references linking between Lommel-Bessel, Log-Gamma and Zeta functions are:
First published version: January 9, 2011 | |||||||||||||||||||||||||||||