Some theta functions identities associated with the modular equations of degree 5.
Sommes de carrés, fonctions L et formes modulaires.
Sommes de Dedekind elliptiques et formes de Jacobi
À partir des formes de Jacobi , on construit une somme de Dedekind elliptique. On obtient ainsi un analogue elliptique aux sommes multiples de Dedekind construites à partir des fonctions cotangentes, étudiées par D. Zagier. En outre, on établit une loi de réciprocité satisfaite par ces nouvelles sommes. Par une procédure de limite, on peut retrouver la loi de réciprocité remplie par les sommes multiples de Dedekind classiques. D’autre part, en les spécialisant en des paramètres de points de 2- division,...
Sommes de Gauss cubiques et revêtements de
Sommes de Gauss et séries thêta
Special values and mixed weight triple products (With an Appendix by Don Blasius).
Special values of Hilbert modular functions.
Recently, Baily has established new foundation for complex multiplication in the context of Hilbert modular functions; see [1]-[4]. However, in his treatment there is a restriction on the class of CM-points treated. Namely, the order of complex multiplications associated to the point must be the maximal order in its quotient field. The purpose of this paper is two-fold: (1) to remove the restriction just mentioned; (2) to recover a result of Tate on the conjugates of CM-points by arbitrary Galois...
Special values of multiple gamma functions
We give a Chowla-Selberg type formula that connects a generalization of the eta-function to with multiple gamma functions. We also present some simple infinite product identities for certain special values of the multiple gamma function.
Special values of symmetric power -functions and Hecke eigenvalues
We compute the moments of -functions of symmetric powers of modular forms at the edge of the critical strip, twisted by the central value of the -functions of modular forms. We show that, in the case of even powers, it is equivalent to twist by the value at the edge of the critical strip of the symmetric square -functions. We deduce information on the size of symmetric power -functions at the edge of the critical strip in subfamilies. In a second part, we study the distribution of small and...
Special values of the elliptic modular function and factorization formulae.
Special values of the standard zeta functions for elliptic modular forms.
Special values of twisted symmetric square -functions and the trace formula
Special values of zeta functions attached to Siegel modular forms
Spectral deformations of automorphic functions over graphs of groups.
Spectral geometry and scattering theory for certain complete surfaces of finite volume.
Spectral limits for hyperbolic surfaces, I.
Spectral limits for hyperbolic surfaces, II.
Spectral theta series of operators with periodic bicharacteristic flow
The theta series is a classical example of a modular form. In this article we argue that the trace , where is a self-adjoint elliptic pseudo-differential operator of order 1 with periodic bicharacteristic flow, may be viewed as a natural generalization. In particular, we establish approximate functional relations under the action of the modular group. This allows a detailed analysis of the asymptotics of near the real axis, and the proof of logarithm laws and limit theorems for its value...
Square Integrable Automorphic Forms and Cohomology of Arithmetic Quotients of SU (p,q).
Stabile Modul formen.