arXiv subjects

Roger Gay

Publications and source records attributed to Roger Gay.

3 recordsLinked to original sources

arXiv2020

Harmonic Analysis of some arithmetical functions

We study three functions which are power series in the variable $z$, Dirichlet series in the variable $s$ and with coefficients given by arithmetical functions. A strong point is to relate these functions to some Hilbert spaces. Three main ingredients are used: an estimate of Davenport on sums of M\"obius functions, a result of Lucht on convolutions of arithmetical Dirichlet series and the introduction of an operation $\otimes$ on power series, naturally associated with the mentioned Hilbert spaces.

math.NT↗

arXiv2020

Arithmetic and Analysis of the series $\displaystyle { \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{x}{n} }$

In this paper we connect a celebrated theorem of Nyman and Beurling on the equivalence between the Riemann hypothesis and the density of some functional space in $ L^2(0, 1)$ to a trigonometric series considered first by Hardy and Littlewood. We highlight some of its curious analytical and arithmetical properties.

math.NT↗

arXiv2013

Sur deux formules de Frobenius et Stickelberger et inversion de Lagrange

We give a proof and extension of two formulas of Frobenius and Stickelberger of Differential Calculus that they used in a fundamental paper concerning elliptic functions theory. Our main ingredient is the introduction of a bilinear form which is a vast generalization of Leibniz formula. This bilinear form is also connected to the Lagrange product formula. As a corollary, we give a different proof of a theorem of P.J. Olver.

math.CA↗