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

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 -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.

**[1]**Raymond Ayoub,*Euler and the zeta function*, Amer. Math. Monthly**81**(1974), 1067–1086. MR**0360116****[2]**Philip J. Davis,*Leonhard Euler’s integral: A historical profile of the gamma function.*, Amer. Math. Monthly**66**(1959), 849–869. MR**0106810****[3]**H. M. Edwards,*Riemann’s zeta function*, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Pure and Applied Mathematics, Vol. 58. MR**0466039****[4]**Nicholas M. Katz,*𝑝-adic 𝐿-functions via moduli of elliptic curves*, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974) Amer. Math. Soc., Providence, R. I., 1975, pp. 479–506. MR**0432649**

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DOI:
https://doi.org/10.1090/S0002-9939-1981-0601719-8

Article copyright:
© Copyright 1981
American Mathematical Society