Abstract
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.
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References
L. Euler: Introductio in Analysin infinitorum, Opera Omnia (1),Vol. 8.
Hardy and Wright, specifically, Chaps. 17 and 19.
A. Weil: Two lectures on Number Theory, Past and Present.
L. Kronecker: Zur Geschichte des Reziprozitätsgesetzes, Werke II, 1–10.
J. Steinig: On Euler’s idoneal numbers, Elem. der Math. 21 (1966), 73–88.
Th. L. Heath: see references to Chap. 2.
J. E. Hofmann: see references to Chap. 2.
A. P. Youschkevitch: Euler, Leonhard (in: Dictionary of Scientific Biography).
N. Fuss: Lobrede auf Herrn Leonhard Euler, in: Euler, Opera Omnia (1),Vol. 1.
Euler-Goldbach: Briefwechsel (Correspondence).
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© 1985 Springer Science+Business Media New York
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Scharlau, W., Opolka, H. (1985). Euler. In: From Fermat to Minkowski. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1867-6_3
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DOI: https://doi.org/10.1007/978-1-4757-1867-6_3
Publisher Name: Springer, New York, NY
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