Explicit Construction of Maass Wave Forms and Their Petersson Inner Products
Abstract
In this paper, we explicitly construct Maass wave cusp forms associated to Hecke characters on arbitrary real quadratic fields. This result is a generalization of Maass (1949), who constructed Maass wave cusp forms under the assumption that narrow class number is one. We also compute its Petersson inner product explicitly and give a few examples involving dihedral Artin representations.
Fields of Study & Subjects
Advanced Algebra and Geometry
Analytic Number Theory Research
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 29 January 2026
- Document type
- Preprint