• Winfried Scharlau
  • Hans Opolka
Part of the Undergraduate Texts in Mathematics book series (UTM)


After 1650 number theory stood virtually still for a hundred years. This period saw the development of analysis in the work of Isaac Newton (1643–1727), Gottfried Wilhelm Leibniz (1646–1716), the Bernoullis (Jacob, 1655–1705; Johann I, 1667–1748; Nicholas II, 1687–1759; Daniel 1700–1792), and Leonhard Euler (1707–1783). Analysis is not the subject of this book, but analytic methods have played an important role in number theory since Dirichlet. This interplay between analysis and number theory has its origins in the work of Euler, and we will try to sketch the beginnings of this development here.


Number Theory Prime Number Elliptic Function Geometrical Series Bernoulli Number 
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  1. L. Euler: Introductio in Analysin infinitorum, Opera Omnia (1),Vol. 8.Google Scholar
  2. Hardy and Wright, specifically, Chaps. 17 and 19.Google Scholar
  3. A. Weil: Two lectures on Number Theory, Past and Present.Google Scholar
  4. L. Kronecker: Zur Geschichte des Reziprozitätsgesetzes, Werke II, 1–10.Google Scholar
  5. J. Steinig: On Euler’s idoneal numbers, Elem. der Math. 21 (1966), 73–88.Google Scholar
  6. Th. L. Heath: see references to Chap. 2.Google Scholar
  7. J. E. Hofmann: see references to Chap. 2.Google Scholar
  8. A. P. Youschkevitch: Euler, Leonhard (in: Dictionary of Scientific Biography).Google Scholar
  9. N. Fuss: Lobrede auf Herrn Leonhard Euler, in: Euler, Opera Omnia (1),Vol. 1.Google Scholar
  10. Euler-Goldbach: Briefwechsel (Correspondence).Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Winfried Scharlau
    • 1
  • Hans Opolka
    • 1
  1. 1.Mathematisches InstitutUniversität MünsterMünsterWest Germany

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