Analytic Number Theory A Tribute to Gauss and Dirichlet Part 1 pdf

Clay Mathematics Proceedings Volume 7 American Mathematical Society Clay Mathematics Institute Analytic Number Theory A Tribute to Gauss and Dirichlet 7 AMS CMI Duke and Tschinkel, Editors 264 pages on 50 lb stock • 1/2 inch spine Analytic Number Theory A Tribute to Gauss and Dirichlet William Duke Yuri Tschinkel Editors CMIP/7 www.ams.org www.claymath.org 4-color process Articles in this volume are based on talks given at the Gauss– Dirichlet Conference held in Göttingen on June 20–24, 2005. The conference commemorated the 150th anniversary of the death of C F. Gauss and the 200th anniversary of the birth of J L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet. Among the topics are the distribution of primes (long arithmetic progres- sions of primes and small gaps between primes), class groups of binary quadratic forms, various aspects of the theory of L-func- tions, the theory of modular forms, and the study of rational and integral solutions to polynomial equations in several variables. Analytic Number Theory A Tribute to Gauss and Dirichlet American Mathematical Society Clay Mathematics Institute Clay Mathematics Proceedings Volume 7 Analytic Number Theory A Tribute to Gauss and Dirichlet William Duke Yuri Tschinkel Editors [...]... offered Dirichlet a teaching position at the University of Breslau (Silesia, now Wroclaw, Poland) with an opportunity for a Habilitation (qualification examination for lecturing at a university) and a modest annual salary of 400 talers, which was the usual starting salary of an associate professor at that time (This was not too bad an offer for a 21- year-old young man without any final examination.) Von Altenstein... statements The present account is intended as a first attempt to remedy this situation 1 Family Background and School Education Johann Peter Gustav Lejeune Dirichlet, to give him his full name, was born in D¨ ren (approximately halfway between Cologne and Aachen (= Aix-la-Chapelle)) u on February 13 , 18 05 He was the seventh1 and last child of Johann Arnold Lejeune Dirichlet (17 62 18 37) and his wife Anna... lavishly illustrated volumes on the scientific evaluation of his 17 99 18 04 research expedition with A Bonpland (17 73 18 58) to South and Central America This expedition had earned him enormous world-wide fame, and he became a corresponding member of the French Academy in 18 04 and a foreign member in 18 10 Von Humboldt took an exceedingly broad interest in the natural sciences and beyond that, and he made... for only one year, starting in winter 18 20, and then left with a school-leaving certificate It has been asserted that Dirichlet passed the Abitur examination, but a check of the documents revealed that this was not the case ([Sc .1] ) The regulations for the Abitur examination demanded that the candidate must be able to carry on a conversation in Latin, which was the lingua franca of the learned world for... life underwent a fundamental change in the summer of 18 23 The General M.S Foy (17 75 18 25) was looking for a private tutor to teach his children the German language and literature The general was a highly cultured brilliant man and famous war hero, who held leading positions for 20 years during the wars of the French Republic and Napol´on Bonaparte He had gained enormous popularity because of e the circumspection... much at ease in this fortunate position The house of General Foy was a meeting-point of many celebrities of the French capital, and this enabled Dirichlet to gain self-assurance in his social bearing, which was of notable importance for his further life Dirichlet soon became acquainted with his academic teachers His first work of academic character was a French translation of a paper by J .A Eytelwein (17 64–... theory ([G .1] , pp 16 9 17 8, 93 14 8, 313 –385; [R]) This was Gauß’ last long paper on number theory, and a very important one, helping to open the gate to algebraic number theory The first printed proof of the biquadratic reciprocity law was published only in 18 44 by G Eisenstein (18 23 18 52; see [Ei], vol 1, pp 14 1 16 3); Jacobi had already given a proof in his lectures in K¨nigsberg o somewhat earlier Dirichlet. .. Hachette (17 69 18 34), and L.B Francœur (17 73 18 49) He also asked for permission to attend lectures as a guest student at the famous ´ Ecole Polytechnique But the Prussian charg´ d a aires in Paris refused to ask for e such a permission without the special authorization from the Prussian minister of religious, educational, and medical a airs, Karl Freiherr von Stein zum Altenstein (17 70 18 40) The 17 -year-old... in mathematics and history, in particular in the then recent history following the French Revolution It may be assumed that Dirichlet s later free and liberal political views can be traced back to these early studies and to his later stay in the house of General Foy in Paris (see sect 3) After two years Dirichlet changed to the Jesuiter-Gymnasium in Cologne Elvenich became a philologist at the Gymnasium... wanted Dirichlet to move to Breslau just a few weeks later since there was a vacancy He added, if Dirichlet had not yet passed the doctoral examination, he might send an application to the philosophical faculty of the University of Bonn which would grant him all facilities consistent with the rules ([Sc .1] ) The awarding of the doctorate, however, took more time than von Altenstein and Dirichlet had . solutions to polynomial equations in several variables. Analytic Number Theory A Tribute to Gauss and Dirichlet American Mathematical Society Clay Mathematics Institute Clay Mathematics Proceedings Volume. Clay Mathematics Proceedings Volume 7 American Mathematical Society Clay Mathematics Institute Analytic Number Theory A Tribute to Gauss and Dirichlet 7 AMS CMI Duke and Tschinkel, Editors 264. modest annual salary of 400 talers, which was the usual starting salary of an associate professor at that time. (This was not too bad an offer for a 21- year-old young man without any final examination.)