Explicit Construction of Maass Wave Forms and Their Petersson Inner Products

Fuente: arXiv
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Main Author: Tanaka, Daichi
Format: Preprint
Published: 2026
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author Tanaka, Daichi
author_facet Tanaka, Daichi
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_21588
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Explicit Construction of Maass Wave Forms and Their Petersson Inner Products
Tanaka, Daichi
Number Theory
Representation Theory
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.
title Explicit Construction of Maass Wave Forms and Their Petersson Inner Products
topic Number Theory
Representation Theory
url https://arxiv.org/abs/2601.21588