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By Duke W.

Articles during this quantity are according to talks given on the Gauss-Dirichlet convention held in Gottingen on June 20, 2005. The convention venerated the a hundred and fiftieth anniversary of the loss of life of C.-F. Gauss and the 2 hundredth anniversary of the beginning of J.-L. Dirichlet. the amount starts off with a definitive precis of the existence and paintings of Dirichlet and maintains with 13 papers through major specialists on examine themes of present curiosity in quantity idea that have been at once encouraged by means 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 varieties, quite a few points of the idea of $L$-functions, the speculation of modular kinds, and the research of rational and critical options to polynomial equations in different variables.

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1837. — Seidel, Philipp Ludwig: Note u ¨ ber eine Eigenschaft der Reihen, welche diskontinuierliche Funktionen darstellen. 1847. (Ostwald’s Klassiker der exakten Wissenschaften 116, ed. by H. G. Lejeune: Ged¨ achtnisrede auf Carl Gustav Jacob Jacobi. Abh. Kgl. Akad. Wiss. Berlin 1852, 1–27; also in J. Reine Angew. Math. 2], pp. J. Jacobi: Gesammelte Werke, vol. 1. W. ) Berlin: Reimer, 1881, pp. 1–28. Reprinted in: Reichardt, H. ): Nachrufe auf Berliner Mathematiker des 19. Jahrhunderts. J. L. E.

Friendship with Liouville Joseph Liouville (1809–1882) was one of the leading French mathematicians of his ´ time. He began his studies at the Ecole Polytechnique when Dirichlet was about to leave Paris and so they had no opportunity to become acquainted with each other during their student days. In 1833 Liouville began to submit his papers to Crelle. This brought him into contact with mathematics in Germany and made him aware of the insufficient publication facilities in his native country. Hence, in 1835, he decided to create a new French mathematical journal, the Journal de Math´ematiques Pures et Appliqu´ees, in short, Liouville’s Journal.

Lejeune: Ged¨ achtnisrede auf Carl Gustav Jacob Jacobi. Abh. Kgl. Akad. Wiss. Berlin 1852, 1–27; also in J. Reine Angew. Math. 2], pp. J. Jacobi: Gesammelte Werke, vol. 1. W. ) Berlin: Reimer, 1881, pp. 1–28. Reprinted in: Reichardt, H. ): Nachrufe auf Berliner Mathematiker des 19. Jahrhunderts. J. L. E. Kummer, L. Kronecker, K. Weierstraß. ) Leipzig: Teubner, 1988, pp. G. G. Lejeune Dirichlet, herausgegeben und mit Zus¨ atzen versehen von R. Dedekind. , improved and enlarged. G. Lejeune: Vorlesungen u ¨ ber die Lehre von den einfachen und mehrfachen bestimmten Integralen, ed.

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