Duke Mathematical Journal

The Eisenstein constant

Bernard M. Dwork and Alfred J. van der Poorten

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Duke Math. J. Volume 65, Number 1 (1992), 23-43.

First available in Project Euclid: 20 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 12H25: $p$-adic differential equations [See also 11S80, 14G20]
Secondary: 11R09: Polynomials (irreducibility, etc.)


Dwork, Bernard M.; van der Poorten, Alfred J. The Eisenstein constant. Duke Math. J. 65 (1992), no. 1, 23--43. doi:10.1215/S0012-7094-92-06502-1. http://projecteuclid.org/euclid.dmj/1077295017.

Export citation


  • [Ar] E. Artin, Algebraic numbers and algebraic functions, Gordon and Breach Science Publishers, New York, 1967.
  • [Chr] G. Christol, Un théorème de transfert pour les disques singuliers réguliers, Astérisque (1984), no. 119-120, 5, 151–168.
  • [ChrDw1] G. Christol and B. Dwork, Effective $p$-adic bounds at regular singular points, Duke Math. J. 62 (1991), no. 3, 689–720.
  • [ChrDw2] G. Christol and B. Dwork, Differential Modules of Bounded Spectral Norm, Contemp. Math., to appear.
  • [DwRo] B. Dwork and P. Robba, On natural radii of $p$-adic convergence, Trans. Amer. Math. Soc. 256 (1979), 199–213.
  • [Die] P. Dienes, The Taylor series: an introduction to the theory of functions of a complex variable, Dover Publications Inc., New York, 1957.
  • [Eis]1 G. Eisenstein, Über eine allgemeine Eigenschaft der Reihen-Entwicklungen aller algebraischen Funktionen, Bericht Königl. Preuß. Akad. Wiss., Berlin, 1852.
  • [Eis]2 G. Eisenstein, Mathematische Werke. Band II, Chelsea Publishing Co., New York, 1975.
  • [Epp] H. P. Epp, Eliminating wild ramification, Invent. Math. 19 (1973), 235–249.
  • [RS] J. Rosser and L. Schoenfeld, Sharper bounds for the Chebyshev functions $\theta (x)$ and $\psi (x)$, Math. Comp. 29 (1975), 243–269.
  • [Sch] O. F. G. Schilling, The Theory of Valuations, Mathematical Surveys, No. 4, American Mathematical Society, New York, N. Y., 1950.
  • [Schm] W. M. Schmidt, Eisenstein's theorem on power series expansions of algebraic functions, Acta Arith. 56 (1990), no. 2, 161–179.
  • [Sh] H. Shapiro, Introduction to the theory of numbers, Pure and Applied Mathematics, John Wiley & Sons Inc., New York, 1983.

See also

  • See also: Bernard M. Dwork, Alfred J. van der Poorten. Corrections to “The Eisenstein constant”. Duke Math. J. Vol. 76, No. 2 (1994), pp. 669–672.