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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Determinant expression of Selberg zeta functions. III
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by Shin-ya Koyama PDF
Proc. Amer. Math. Soc. 113 (1991), 303-311 Request permission

Abstract:

We will prove that for $\operatorname {PSL(2},{\mathbf {R}})$ and its cofinite subgroup, the Selberg zeta function is expressed by the determinant of the Laplacian. We will also give an explicit calculation in case of congruence subgroups, and deduce that the part of the determinant of the Laplacian composed of the continuous spectrum is expressed by Dirichlet $L$-functions.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 303-311
  • MSC: Primary 11F72
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1062391-5
  • MathSciNet review: 1062391