Arithmetic equivalents
著者
書誌事項
Arithmetic equivalents
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 164 . Equivalents of the Riemann hypothesis ; v. 1）
Cambridge University Press, 2017
- : hardback
大学図書館所蔵 件 / 全37件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
ISBN for Equivalents of the Riemann hypothesis: 9781108290784
Includes bibliographical references (p. 313-320) and index
内容説明・目次
内容説明
The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.
目次
- 1. Introduction
- 2. The Riemann Zeta function
- 3. Estimates
- 4. Classical equivalences
- 5. Euler's Totient function
- 6. A variety of abundant numbers
- 7. Robin's theorem
- 8. Numbers which do not satisfy Robin's inequality
- 9. Left, right and extremely abundant numbers
- 10. Other equivalents to the Riemann hypothesis
- Appendix A. Tables
- Appendix B. RHpack mini-manual
- Bibliography
- Index.
「Nielsen BookData」 より
