Explicit Construction of Maass Wave Forms and Their Petersson Inner Products
Number Theory
2026-02-04 v3 Representation Theory
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.
Keywords
Cite
@article{arxiv.2601.21588,
title = {Explicit Construction of Maass Wave Forms and Their Petersson Inner Products},
author = {Daichi Tanaka},
journal= {arXiv preprint arXiv:2601.21588},
year = {2026}
}