Eisenstein series modulo p2
Journal article, 2025
We study congruences for Eisenstein series on SL2 (ℤ) modulo p2 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.
modular form congruences
Eisenstein series
Eichler-Shimura relations
Author
Scott Ahlgren
University of Illinois
Michael Hanson
University of North Texas
Martin Raum
University of Gothenburg
Chalmers, Mathematical Sciences, Algebra and geometry
Olav K. Richter
University of North Texas
Forum Mathematicum
0933-7741 (ISSN) 1435-5337 (eISSN)
Vol. In PressFourier coefficients of Siegel modular forms of block-diagonal index
Swedish Research Council (VR) (2023-04217), 2024-01-01 -- 2027-12-31.
Subject Categories (SSIF 2025)
Discrete Mathematics
Subatomic Physics
DOI
10.1515/forum-2024-0470