A simple approach to the analytic continuation and values at negative integers for Riemann’s zeta function
HTML articles powered by AMS MathViewer
- by David Goss PDF
- Proc. Amer. Math. Soc. 81 (1981), 513-517 Request permission
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
- Raymond Ayoub, Euler and the zeta function, Amer. Math. Monthly 81 (1974), 1067–1086. MR 360116, DOI 10.2307/2319041
- Philip J. Davis, Leonhard Euler’s integral: A historical profile of the gamma function, Amer. Math. Monthly 66 (1959), 849–869. MR 106810, DOI 10.2307/2309786
- H. M. Edwards, Riemann’s zeta function, Pure and Applied Mathematics, Vol. 58, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1974. MR 0466039
- 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
Additional Information
- © Copyright 1981 American Mathematical Society
- 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