Eisenstein series modulo p2

被引：0

作者：

Ahlgren, Scott ^{[2
]}

Hanson, Michael ^{[3
]}

Raum, Martin ^{[1
]}

Richter, Olav K. ^{[3
]}

机构：

[1] Chalmers Tekn Hogskolaoch Goteborgs Univ, Inst Matemat Vetenskaper, S-41296 Gothenburg, Sweden

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[3] Univ North Texas, Dept Math, Denton, TX 76203 USA

来源：

FORUM MATHEMATICUM | 2025年

关键词：

Eisenstein series; modular form congruences; Eichler-Shimura relations;

D O I：

10.1515/forum-2024-0470

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study congruences for Eisenstein series on SL2(Z) modulo p2, where p = 5 is prime. It is classically known that all Eisenstein series of weight at least 4 are determined modulo p2 by those of weight at most p2 - p + 2. We prove that up to powers of Ep-1, each such Eisenstein series is in fact determined modulo p2 by a modular form of weight at most 2p - 4. We also determine E2 modulo p2 in terms of a modular form of weight p + 1.

引用

页数：10

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