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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the analytic continuation of the Minakshisundaram-Pleijel zeta function for compact Riemann surfaces
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by Burton Randol PDF
Trans. Amer. Math. Soc. 201 (1975), 241-246 Request permission

Abstract:

A formula is derived for the Minakshisundaram-Pleijel zeta function in the half-plane Re $s < 0$.
References
  • Michio Kuga, Topological analysis and its applications in weakly symmetric Riemannian spaces. (Introduction to the work of A. Selberg.), Sūgaku 9 (1957/58), 166–185 (Japanese). MR 103171
  • H. P. McKean, Selberg’s trace formula as applied to a compact Riemann surface, Comm. Pure Appl. Math. 25 (1972), 225–246. MR 473166, DOI 10.1002/cpa.3160250302
  • S. Minakshisundaram and Å. Pleijel, Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds, Canad. J. Math. 1 (1949), 242–256. MR 31145, DOI 10.4153/cjm-1949-021-5
  • A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47–87. MR 88511
  • G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 201 (1975), 241-246
  • MSC: Primary 10H10; Secondary 30A16, 58G99
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0369286-6
  • MathSciNet review: 0369286