Weight $1/2$ multiplier systems for the group $\Gamma_0^+(p)$ and a geometric formulation

Michael H. Mertens; Mark A. Norfleet

Weight $1/2$ multiplier systems for the group $\Gamma_0^+(p)$ and a geometric formulation

Number Theory 2023-05-23 v1 Geometric Topology

Authors: Michael H. Mertens , Mark A. Norfleet

Abstract

We construct a weight $1/2$ multiplier system for the group $\Gamma_0^+(p)$ , the normalizer of the congruence subgroup $\Gamma_0(p)$ where $p$ is an odd prime, and we define an analogue of the eta function and Rademacher symbol and relate it to the geometry of edge paths in a triangulation of the upper half plane.

Keywords

weight 1/2 multiplier system gamma_0^+(p) eta function rademacher symbol edge paths upper half plane congruence subgroup

Cite

@article{arxiv.2305.13196,
  title  = {Weight $1/2$ multiplier systems for the group $\Gamma_0^+(p)$ and a geometric formulation},
  author = {Michael H. Mertens and Mark A. Norfleet},
  journal= {arXiv preprint arXiv:2305.13196},
  year   = {2023}
}

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9 pages

Weight $1/2$ multiplier systems for the group $\Gamma_0^+(p)$ and a geometric formulation

Abstract

Keywords

Cite

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