On congruence $L$ -series.

A Generalization of Wolstenholme’s Harmonic Series Congruence

Let A, B be two non-zero integers.

On the transfer congruence between p-adic Hecke L-functions

We prove the transfer congruence between p-adic Hecke L-functions for CM fields over cyclotomic extensions, which is a non-abelian generalization of the Kummer’s congruence. The ingredients of the proof include the comparison between Hilbert modular varieties, the q-expansion principle, and some modification of Hsieh’s Whittaker model for Katz’ Eisenstein series. As a first application, we prov...

On l-adic representations attached to non-congruence subgroups II

In this paper we extend the results of [9] to two other subgroups of SL2(Z). Let Γ ⊂ SL2(Z) be a subgroup of finite index. In [8] and [9] it is shown how to attach to the space of cusp forms of weight w on Γ (whose dimension we denote by d) a strictly compatible family {ρl} of 2d-dimensional l-adic representations of Gal(Q/K), for a certain number field, mildly generalising the representations ...

On Approximation by L Uroth Series

par Karma DAJANI et Cor KRAAIKAMP R esum e. Pour x 2]0; 1], on note p n =q n la suite des convergents de la s erie de L uroth associ ee, et on d eenit par n = q n x ? p n , n 1 ses coeecients d'approximation. Dans BBDK], on d etermine la fonction de r epartition limite de la suite (n), en utilisant l'extension naturelle du syst eme ergodique sous-jacent au d evelop-pement en s erie de L uroth. ...

A q-Analogue of Wolstenholme's Harmonic Series Congruence