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A simple approach to the analytic continuation and values at negative integers for Riemann's zeta function


Author: David Goss
Journal: Proc. Amer. Math. Soc. 81 (1981), 513-517
MSC: Primary 10H05
DOI: https://doi.org/10.1090/S0002-9939-1981-0601719-8
MathSciNet review: 601719
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Abstract: In this paper, the author presents a new approach to the subjects in the title, putting them in a new light. In fact, only integration by parts is used. This approach has two advantages: (1) it makes the $ p$-adic theory seem even more natural, and (2) it is accessible to readers with only one year of basic calculus, making the subjects reachable in elementary courses.


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

  • [1] R. Ayoub, Euler and the zeta-function, Amer. Math. Monthly 81 (1974), 1067-1086. MR 0360116 (50:12566)
  • [2] P. Davis, Leonhard Euler's integral: A historical profile of the gamma function, Amer. Math. Monthly 66 (1959), 849-869. MR 0106810 (21:5540)
  • [3] H. M Edwards, Riemann's zeta-function, Academic Press, New York, 1974. MR 0466039 (57:5922)
  • [4] N. Katz, $ P$-adic $ L$-functions via moduli of elliptic curves, Proc. Sympos. Pure Math., vol. 29, Amer. Math. Soc., Providence, R. I., 1975, pp. 479-506. MR 0432649 (55:5635)

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DOI: https://doi.org/10.1090/S0002-9939-1981-0601719-8
Article copyright: © Copyright 1981 American Mathematical Society

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