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arXiv · 2601.21588

Explicit Construction of Maass Wave Forms and Their Petersson Inner Products

Daichi Tanaka
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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.

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Daichi Tanaka. 2026-01-29. Explicit Construction of Maass Wave Forms and Their Petersson Inner Products. https://arxiv.org/abs/2601.21588

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