Arithmetic tales

著者

• Bordellès, Olivier

書誌事項

Arithmetic tales

Olivier Bordellès ; [translated by Véronique Bordellès]

（Universitext）

Springer, c2020

Advanced ed

注記

"2nd ed."--Spine

Includes bibliographical references and index

内容説明・目次

内容説明

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 a 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.

目次

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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BC04461309
• ISBN:
  • 9783030549459
• 出版国コード: sz
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cham
• ページ数/冊数: xix, 782 p.
• 大きさ: 24 cm
• 分類:
  • DC23 : 512.7
• 件名:
  • LCSH : Number theory
• 親書誌ID:
  • BA00021004