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Arithmetic tales: advanced edition

This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses. Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller trea...

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Detalles Bibliográficos
Autor principal: Bordellès, Olivier
Lenguaje:eng
Publicado: Springer 2020
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-030-54946-6
http://cds.cern.ch/record/2746911
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author Bordellès, Olivier
author_facet Bordellès, Olivier
author_sort Bordellès, Olivier
collection CERN
description This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses. Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results. Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.
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spelling cern-27469112021-04-21T16:44:17Zdoi:10.1007/978-3-030-54946-6http://cds.cern.ch/record/2746911engBordellès, OlivierArithmetic tales: advanced editionMathematical Physics and MathematicsThis textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses. Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results. Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.Springeroai:cds.cern.ch:27469112020
spellingShingle Mathematical Physics and Mathematics
Bordellès, Olivier
Arithmetic tales: advanced edition
title Arithmetic tales: advanced edition
title_full Arithmetic tales: advanced edition
title_fullStr Arithmetic tales: advanced edition
title_full_unstemmed Arithmetic tales: advanced edition
title_short Arithmetic tales: advanced edition
title_sort arithmetic tales: advanced edition
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-030-54946-6
http://cds.cern.ch/record/2746911
work_keys_str_mv AT bordellesolivier arithmetictalesadvancededition