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Complex powers of the Laplace operator on the circle


Author: Jack Morava
Journal: Proc. Amer. Math. Soc. 94 (1985), 213-216
MSC: Primary 58G05; Secondary 11M35
DOI: https://doi.org/10.1090/S0002-9939-1985-0784165-X
MathSciNet review: 784165
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Abstract: The classical zeta function of Lerch has an analytic continuation as a distribution on the circle which seems to be very different from its usual analytic continuation: for example, the Bernoulli polynomials come out upside down.


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  • [1] B. Berndt, Two new proofs of Lerch's functional equation, Proc. Amer. Math. Soc. 32 (1972), 403-408. MR 0297721 (45:6773)
  • [2] I. M. Gel'fand and G. E. Šilov, Generalised functions, Vol. I, Academic Press, New York, 1964.
  • [3] D. Kubert and S. Lang, Modular units, Grundlehren Math. Wiss., Band 244, Springer, Berlin, 1981. MR 648603 (84h:12009)
  • [4] S. Lang, Units and class groups in number theory and algebraic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), 253-316 (appendix). MR 648522 (83m:12002)
  • [5] M. Lerch, Zakladové theorie Malmstenovskych rad, Rozpravy Československé Akad. Cišure Frantiska Josefa 27 (1892), 525-592.
  • [6] J. Milnor, Polylogarithms, the Hurwitz zeta-function and the Kubert identities, Enseign. Math. 29 (1983), 281-322. MR 719313 (86d:11007)
  • [7] D. Ramakrishnan, On the monodromy of higher logarithms, Proc. Amer. Math. Soc. 85 (1982), 596-599. MR 660611 (84b:53049)
  • [8] P. Ramond, Field theory: a modern primer, Princeton Frontiers in Physics 57 (1981). MR 602697 (84h:81077)
  • [9] L. Schwartz, Théorie des distributions, Vol. II, Hermann, Paris, 1966. MR 0209834 (35:730)
  • [10] R. T. Seeley, Complex powers of elliptic operators, Proc. Sympos. Pure Math., Vol. 10, Amer. Math. Soc., Providence, R.I., 1967, pp. 288-308. MR 0237943 (38:6220)
  • [11] C. L. Siegel, Lectures on advanced analytic number theory, Tata Institute, Bombay, 1961. MR 0262150 (41:6760)
  • [12] B. Simon, Trace ideals and applications, London Math. Soc. Lecture Notes 35, Cambridge Univ. Press, 1979. MR 541149 (80k:47048)
  • [13] E. R. Speer, Generalized Feynman amplitudes, Ann. of Math. Stud., Vol. 62, Princeton Univ. Press, Princeton, N. J., 1969. MR 0241077 (39:2422)
  • [14] E. C. Titchmarsh, Theory of functions, Oxford Univ. Press, New York and London, 1932.
  • [15] A. Weil, Elliptic functions according to Kronecker and Eisenstein, Springer-Verlag, Berlin and New York, 1976. MR 0562289 (58:27769a)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0784165-X
Article copyright: © Copyright 1985 American Mathematical Society

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