Equivariant primitives of Eisenstein series for congruence subgroups
Abstract
We study equivariant primitives of Eisenstein series for principal congruence subgroups and show that they are precisely the corresponding non-holomorphic Eisenstein series. We present closed formulas that naturally generalise existing results for the full modular group. We also focus on Eisenstein series of weight two in the case where the modular curve has genus zero. We show that in those cases the non-holomorphic Eisenstein series of weight two can be written as single-valued logarithms whose argument is a rational function of the Hauptmodul.
Fields of Study & Subjects
Advanced Mathematical Identities
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Communications in Number Theory and Physics
- Publisher
- International Press of Boston
- Volume
- 20
- Issue
- 1
- Pages
- 193–228
- Publication date
- 1 January 2026
- Language
- EN