Arithmetic Tales : Advanced Edition. 2nd ed. 2020
- 種類:
- 電子ブック
- 責任表示:
- by Olivier Bordellès
- 出版情報:
- Cham : Springer International Publishing : Imprint: Springer, 2020
- 著者名:
- シリーズ名:
- Universitext ;
- ISBN:
- 9783030549466 [3030549461]
- 注記:
- 1 Basic Tools -- 2 Linear Diophantine Equations -- 3 Prime Numbers -- 4 Arithmetic Functions -- 5 Lattice Points -- 6 Exponential Sums -- 7 Algebraic Number Fields. Hints and Answers to Exercises -- Index.
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 - ローカル注記:
- 岐阜大学構成員専用E-BOOKS (Gifu University members only)
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