By Yves Meyer
A zeta function is associated with any even crystalline measure $\mu$ on $\mathbb{R}$. If $\mathcal{F}(\mu)=\mu$ where $\mathcal{F}$ denotes the Fourier transform this zeta function satisfies the same functional equation as the Riemann zeta function. Does the converse implication hold? Let $\phi(s)=\Sigma^\infty_1 a_k \lambda^{-s}_k$ be a Dirichlet series. One assumes that $\phi(s)$ satisfies the same functional equation as the Riemann zeta function. Does there exist an even crystalline measure $\mu$ which generates $\phi$ and such that $\mathcal{F}(\mu)=\mu$? Kahane and Mandelbrojt addressed this issue. A solution is given in this talk.
By Sylvie Benzoni-Gavage , Lise Øvreås
By Nalini Anantharaman
By Albert Schwarz
By Albert Schwarz
By Albert Schwarz
By Albert Schwarz
By Juan Camilo Arosemena Serrato
By Pieter Spaas
By Francesca Arici
By Shirly Geffen
By Amine Marrakchi
