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On the analytic continuation of the Minakshisundaram-Pleijel zeta function for compact Riemann surfaces


Author: Burton Randol
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
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Abstract: A formula is derived for the Minakshisundaram-Pleijel zeta function in the half-plane Re $ s < 0$.


References [Enhancements On Off] (What's this?)

  • [1] Michio Kuga, Topological analysis and its applications in weakly symmetric Riemannian spaces. (Introduction to the work of A. Selberg.), Sûgaku 9 (1957/1958), 166–185 (Japanese). MR 0103171
  • [2] H. P. McKean, Selberg’s trace formula as applied to a compact Riemann surface, Comm. Pure Appl. Math. 25 (1972), 225–246. MR 0473166, https://doi.org/10.1002/cpa.3160250302
  • [3] S. Minakshisundaram and Å. Pleijel, Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds, Canadian J. Math. 1 (1949), 242–256. MR 0031145
  • [4] 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 0088511
  • [5] 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

DOI: https://doi.org/10.1090/S0002-9947-1975-0369286-6
Article copyright: © Copyright 1975 American Mathematical Society

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