On the congruences of Eisenstein series with polynomial indexes

被引：0
|
作者：
Hu, Su [1 ]
Kim, Min-Soo [2 ]
Sha, Min [3 ]
机构：
[1] South China Univ Technol, Dept Math, Guangzhou 510640, Peoples R China
[2] Kyungnam Univ, Dept Math Educ, Chang Won 51767, Gyeongnam, South Korea
[3] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China
来源：
RAMANUJAN JOURNAL | 2023年 / 62卷 / 02期
基金：
新加坡国家研究基金会;
关键词：
Eisenstein series; Congruences; Serre's p-adic family of Eisenstein series; p-adic analysis; Bernoulli numbers;
D O I：
10.1007/s11139-023-00731-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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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页码：413 / 430
页数：18
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