Biró, András and Tóth, Dávid Ákos (2025) On the geometric trace of a generalized Selberg trace formula. FORUM MATHEMATICUM, 37 (2). pp. 547-579. ISSN 0933-7741
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Abstract
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, 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, 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.
| Item Type: | Article |
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| Additional Information: | Funding Agency and Grant Number: National Research, Development and Innovation Office [BMENCTKP2020]; Ministry of Innovation and Technology and the National Research, Development and Innovation Office within the Artificial Intelligence National Laboratory of Hungary; MTA-RI Lenduelet "Momentum" Analytic Number Theory and Representation Theory Research Group; NKFIH (National Research, Development andInnovation Office) [FK 135218, K135885, K 143876]; Renyi IntezetLenduelet Automorphic Research Group Funding text: The research reported in this paper is supported by the "TKP2020, National Challenges Program" of the National Research, Development and Innovation Office (BMENCTKP2020) and by the Ministry of Innovation and Technology and the National Research, Development and Innovation Office within the Artificial Intelligence National Laboratory of Hungary. It is also supported by the MTA-RI Lenduelet "Momentum" Analytic Number Theory and Representation Theory Research Group, by the NKFIH (National Research, Development andInnovation Office) grants FK 135218 (David Toth), K135885 and K 143876 (Andras Biro) and by the Renyi IntezetLenduelet Automorphic Research Group. Online kiadás 2024 |
| Uncontrolled Keywords: | Mathematics, Applied; Selberg trace formula; discrete subgroups of PSL(2, R)(n); |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 05 Feb 2026 10:20 |
| Last Modified: | 05 Feb 2026 10:20 |
| URI: | https://real.mtak.hu/id/eprint/233369 |
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