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The course will cover some classic as well as some recent results of analytic and combinatorial number theory.
Last update: T_KAM (27.04.2005)
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Students learn several fundamental results of analytic and combinatorial number theory and get familiar with the corresponding techniques. Last update: T_KAM (20.04.2008)
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Oral exam, with written preparation. Exam question are/will be given on the course page, see teacher's web page. ************************************************************************ As to situation caused by the current coronavirus pandemia in spring and summer 2020. Form of exam (contact or distant) will be determined for each term in SIS according to actual situation. Contact exam will be writen one with possible oral part. For this course the contact form in small groups (<6, <11 people) appears probable. Last update: Klazar Martin, doc. RNDr., Dr. (14.05.2020)
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G. Tenenbaum: Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press 1995.
Further references will be given in the lecture. Last update: T_KAM (20.04.2008)
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Oral exam, with written preparation. Exam question are/will be given on the course page, see teacher's web page. ************************************************************************ As to situation caused by the current coronavirus pandemia in spring and summer 2020. Form of exam (contact or distant) will be determined for each term in SIS according to actual situation. Contact exam will be writen one with possible oral part. For this course the contact form in small groups (<6, <11 people) appears probable. Last update: Klazar Martin, doc. RNDr., Dr. (14.05.2020)
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The course will consist of a selection of the following topics. Prime number theorem. Dirichlet's theorem on primes in arithmetic progressions. Irrationality of zeta(3). Introduction to modular forms. Shnirelman's theorem on primes and Selberg's sieve. Vinogradov's three primes theorem. Freiman's theorem in additive number theory. T. Tao's proof of Szemeredi's theorem on arithmetic progressions, ... Last update: T_KAM (27.04.2005)
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