On the congruences of Eisenstein series with polynomial indexes

摘要

In this paper, based on Serre's p-adic family of Eisenstein series, we prove a general family of congruences for Eisenstein series Gk in the formS(n) (i=1) gi(p)G fi (p) = g0(p)(mod pN),where f(1)(t), ... , f(n)(t) E Z[t] are non-constant integer polynomials with positive leading coefficients and g0(t), ... , gn(t) E Q(t) are rational functions. This generalizes the classical von Staudt-Clausen and Kummer congruences of Eisenstein series, and also some new Congruences.

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