Analytic number theory: a tribute to Gauss and Dirichlet by William Duke, Yuri Tschinkel

By William Duke, Yuri Tschinkel

Articles during this quantity are according to talks given on the Gauss-Dirichlet convention held in Göttingen 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 lifestyles and paintings of Dirichlet and keeps with 13 papers via top specialists on examine themes of present curiosity in quantity conception that have been without delay stimulated through 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, a number of facets of the speculation of $L$-functions, the speculation of modular types, and the research of rational and quintessential ideas to polynomial equations in different variables. Titles during this sequence are co-published with the Clay arithmetic Institute (Cambridge, MA).

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After his death the sheet was found among his papers. The year 1851 again proved to be a catastrophic one: Jacobi died quite unexpectedly of smallpox the very same day, that little Felix, a son of Felix Mendelssohn Bartholdy, was buried. 2], pp. 133–134). 5]). 12. Dirichlet in G¨ ottingen When Gauß died on February 23, 1855, the University of G¨ ottingen unanimously wanted to win Dirichlet as his successor. 7], p. 121, footnote 3). Moreover it is said that Dirichlet had declared his willingness to accept the call to G¨ ottingen and that he did not want to revise his decision thereafter.

French translation by G. Lejeune Dirichlet: Sur le mouvement de l’eau, en ayant ´egard ` a la contraction qui a lieu au passage par divers orifices, et ` a la r´ esistance qui retarde le mouvement le long des parois des vases. : Dirichlet’s contributions to mathematical probability theory. Hist. Math. : Thomas Archer Hirst — Mathematician Xtravagant. Amer. Math. Monthly 100, I. 435–441, II. 531–538, III. 619–625, IV. 723–731, V. 827–834, VI. : Werke. Zweiter Band. Second Printing. : Sechs Beweise des Fundamentaltheorems u ¨ ber quadratische Reste.

The author is grateful to Ulrich Derenthal for helping to prepare the following table.

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