Explicit Construction of Maass Wave Forms and Their Petersson Inner Products
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915769664667648 |
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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 |