Eisenstein series modulo p2
Artikel i vetenskaplig tidskrift, 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
Författare
Scott Ahlgren
University of Illinois
Michael Hanson
University of North Texas
Martin Raum
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Algebra och geometri
Olav K. Richter
University of North Texas
Forum Mathematicum
0933-7741 (ISSN) 1435-5337 (eISSN)
Vol. In PressFourierkoefficienter för Siegel-modulära former av blockdiagonalt index
Vetenskapsrådet (VR) (2023-04217), 2024-01-01 -- 2027-12-31.
Ämneskategorier (SSIF 2025)
Diskret matematik
Subatomär fysik
DOI
10.1515/forum-2024-0470