Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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] 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10H05

Retrieve articles in all journals with MSC: 10H05

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society