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On the analytic continuation of the Minakshisundaram-Pleijel zeta function for compact Riemann surfaces. (English) Zbl 0299.30010

30B50 Dirichlet series, exponential series and other series in one complex variable
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
30F10 Compact Riemann surfaces and uniformization
11M35 Hurwitz and Lerch zeta functions
Full Text: DOI
[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).
[2] H. P. McKean, Selberg’s trace formula as applied to a compact Riemann surface, Comm. Pure Appl. Math. 25 (1972), 225 – 246. , https://doi.org/10.1002/cpa.3160250302 H. P. McKean, Correction to: ”Selberg’s trace formula as applied to a compact Riemann surface” (Comm. Pure Appl. Math. 25 (1972), 225 – 246), Comm. Pure Appl. Math. 27 (1974), 134. · Zbl 0317.30018
[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. · Zbl 0041.42701
[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. · Zbl 0072.08201
[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. · Zbl 0063.08184
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