Eisenstein series modulo prime powers
Abstract
If p ≥ 5 p\geq 5 is prime and k ≥ 4 k\geq 4 is an even integer with ( p − 1 ) ∤ k (p-1)\nmid k we consider the Eisenstein series G k G_k on S L 2 ( Z ) SL_2(\mathbb {Z}) modulo powers of p p . It is classically known that for such k k we have G k ≡ G k ′ ( mod p ) G_k\equiv G_{k’}\pmod p if k ≡ k ′ ( mod p − 1 ) k\equiv k’\pmod {p-1} . Here we obtain a generalization modulo prime powers p m p^m by giving an expression for G k ( mod
Fields of Study & Subjects
Advanced Mathematical Identities
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Proceedings of the American Mathematical Society Series B
- Volume
- 13
- Issue
- 7
- Pages
- 1–13
- Publication date
- 12 June 2026
- Language
- EN