Intégration de Hecke de fonctions singulières

Abstract

Consider a modular curve Y associated to a congruence subgroup of level N. The Hecke correspondences T n , for (n,N)=1, are defined on Y. For z 1 ∈Y, the sequence of measures T n ¯z 1 =(degT n ) -1 ∑δ z i , T n z 1 being the sum (with multiplicities) of the z i , converges to the invariant normalised measure on Y for the weak topology, viz., the evaluation against functions f∈C c (Y). Here this is extended to the evaluation against a function f that has a logarithmic singularity at a given point. For f given, the convergence is then achieved for almost all z 1 . The proof relies on Sobolev theory, already used in this context in [5, §8].

Locations

• Annales de la faculté des sciences de Toulouse Mathématiques - View - PDF