By Duke W., Tschinkel Y. (eds.)

Articles during this quantity are according to talks given on the Gauss-Dirichlet convention held in GÃ¶ttingen on June 20-24, 2005. The convention venerated the one hundred and fiftieth anniversary of the demise of C.-F. Gauss and the 2 hundredth anniversary of the delivery of J.-L. Dirichlet. the quantity starts with a definitive precis of the existence and paintings of Dirichlet and maintains with 13 papers by way of top specialists on learn subject matters of present curiosity in quantity concept that have been at once stimulated by way of Gauss and Dirichlet. one of the issues are the distribution of primes (long mathematics progressions of primes and small gaps among primes), classification teams of binary quadratic types, quite a few elements of the idea of $L$-functions, the idea of modular kinds, and the learn of rational and necessary recommendations to polynomial equations in different variables. Titles during this sequence are co-published with the Clay arithmetic Institute (Cambridge, MA).

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99). 2], p. 343). A special feature of Dirichlet’s work is his admirable combination of surprisingly simple observations with penetrating thought which led him to deep results. A striking example of such a simple observation is the so-called Dirichlet box principle (also called drawer principle or pigeon-hole principle), which states that whenever more than n objects are distributed in n boxes, then there will be at least one box containing two objects. 1], pp. 633–638), in which he proves the following generalization of a well-known theorem on rational approximation of irrational numbers: Suppose that the real numbers α1 , .

Richard Dedekind, 1831/1981. Eine W¨ urdigung zu seinem 150. Geburtstag. G. Lejeune Dirichlet. Biographische Mitteilungen zum Werdegang Dirichlets. NTM, Schriftenr. Gesch. Naturwiss. Tech. Med. : Die Erinnerungen von Karl Emil Gruhl (1833–1917) an sein Studium der ¨ Mathematik und Physik in Berlin (1853–1856). Jahrb. , Math. Surv. : The three parts of the Dirichlet Nachlass. Hist. Math. 13, 52–56 (1986) [Se] Seguier, J. de: Formes quadratiques et multiplication complexe. L. : Lejeune Dirichlet and the birth of analytic number theory: 1837–1839.

Liouville directed it single-handedly for almost 40 years — the journal enjoys a high reputation to this day. In summer 1839 Dirichlet was on vacation in Paris, and he and Liouville were invited for dinner by Cauchy. It was probably on this occasion that they made each other’s acquaintance, which soon developed into a devoted friendship. After his return to Berlin, Dirichlet saw to it that Liouville was elected a corresponding member6 of the Academy of Sciences in Berlin, and he sent a letter to Liouville suggesting that they should enter into a scientiﬁc correspondence ([L¨ u], p.