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Dirichlet

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Abstract

“... Dirichlet created a new part of mathematics, the application of those infinite series which Fourier has introduced in the theory of heat to the exploration of the properties of the prime numbers. He has discovered a variety of theorems which... are the pillars of new theories.” This is what on December 21, 1846 C. G. J. Jacobi wrote in a letter to Alexander von Humboldt. Today, Dirichlet’s techniques in number theory are more alive than ever.

Keywords

  • Prime Number
  • Meromorphic Function
  • Class Number
  • Dirichlet Series
  • Prime Element

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  • G. P. L. Dirichlet: Werke,particularly the papers: Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Faktor sind, unendlich viele Primzahlen enthält, 1837. Sur la manière de résoudre l’équation t2pn 2 = 1 au moyen des fonctions circulaires, 1837. Recherches sur diverses applications de l’analyse infinitésimale à la théorie des nombres, 1839/40.

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  • O. Ore: Dirichlet, Gustav Peter Lejeune in Dictionary of Scientific Biography.

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  • E. Kummer: Gedächtnisrede auf Gustav Peter Lejeune Dirichlet, Dirichlet’s Works or Kummer’s Works.

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  • H. Minkowski: Peter Gustav Lejeune Dirichlet und seine Bedeutung für die heutige Mathematik. Gesammelte Abhandlungen II.

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  • K.-R. Biermann: Johann Peter Gustav Lejeune Dirichlet, Dokumente für sein Leben und Wirken. Abh. Deutsche Akad. Wiss. Berlin, Klasse für Mathematik, Physik und Technik, Akademie-Verlag, Berlin, 1959.

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© 1985 Springer Science+Business Media New York

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Scharlau, W., Opolka, H. (1985). Dirichlet. In: From Fermat to Minkowski. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1867-6_8

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  • DOI: https://doi.org/10.1007/978-1-4757-1867-6_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-2821-4

  • Online ISBN: 978-1-4757-1867-6

  • eBook Packages: Springer Book Archive