Let 1∕2≤β<1, p be a generic prime number and fβ random multiplicative function supported on the squarefree integers such that (fβ(p))p is an i.i.d. sequence of variables with distribution P(f(p)=−1)=β=1−P(f(p)=+1). Fβ Dirichlet series fβ. We prove formula involving measure-preserving transformations relates Riemann ζ Fβ, for certain values β, give application. Further, we hypothesis connected m...

This paper is a report on work in progress rather than a description of theorems which have attained their final form. The results I shall describe are part of an attempt to continue to higher dimensions the study of the relation between the Hasse-Weil zeta-functions of Shimura varieties and the Euler products associated to automorphic forms, which was initiated by Eichler, and extensively deve...

In this paper, we reinterpret the Colmez conjecture on Faltings’ height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving Faltings’ height of a CM abelian surface and arithmetic intersection numbers, and prove that Colmez’s conjecture for CM abelian surfaces is equivalent to the cuspitality of this modular form.

Dans cet article, nous présentons une nouvelle preuve du théorème central limite de Selberg pour les fonctions L Dirichlet, basée sur méthode Radziwi?? et Soundararajan. De plus, étudions la propriété d’indépendance variables aléatoires apparaissant dans ce théoréme limite.

Let $(\lambda_f(n))_{n\geq 1}$ be the Hecke eigenvalues of either a holomorphic eigencuspform or Hecke-Maass cusp form $f$. We prove that, for any fixed $\eta>0$, under Ramanujan-Petersson conjecture $\rm GL_2$ Maass forms, Rankin-Selberg coefficients $(\lambda_f(n)^2)_{n\geq admit level distribution $\theta=2/5+1/260-\eta$ in arithmetic progressions.