On the geometric trace of a generalized Selberg trace formula
| Autor: | Biró, András, Tóth, Dávid |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A certain generalization of the Selberg trace formula was proved by the first named author in 1999. In this generalization instead of considering the integral of $K(z,z)$ (where $K(z,w)$ is an automorphic kernel function) over the fundamental domain, one considers the integral of $K(z,z)u(z)$, where $u(z)$ is a fixed automorphic eigenfunction of the Laplace operator. This formula was proved for discrete subgroups of $PSL(2,\mathbb{R})$, and just as in the case of the classical Selberg trace formula it was obtained by evaluating in two different ways ("geometrically" and "spectrally") the integral of $K(z,z)u(z)$. In the present paper we work out the geometric side of a further generalization of this generalized trace formula: we consider the case of discrete subgroups of $PSL(2,\mathbb{R})^n$ where $n>1$. Many new difficulties arise in the case of these groups due to the fact that the classification of conjugacy classes is much more complicated for $n>1$ than in the case $n=1$. Comment: 38 pages, 0 figures |
| Databáze: | arXiv |
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