Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents

ISBN-13: 9781107197046 / Angielski / Twarda / 2017 / 336 str.

Kevin Broughan

Opis

This first volume of two presents classical and modern arithmetic equivalents to the Riemann hypothesis. Accompanying software is online.

Recenzje

'This two volume catalogue of many of the various equivalents of the Riemann Hypothesis by Kevin Broughan is a valuable addition to the literature ... all in all these two volumes are a must have for anyone interested in the Riemann Hypothesis.' Steven Decke, MAA Reviews

Spis treści

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.

O autorze

Broughan, Kevin
Kevin Broughan is Emeritus Professor in the Department of Mathematics and Statistics at the University of Waikato, New Zealand. In these two volumes he has used a unique combination of mathematical knowledge and skills. Following the publication of his Columbia University thesis, he worked on problems in topology before undertaking work on symbolic computation, leading to development of the software system SENAC. This led to a symbolic-numeric dynamical systems study of the zeta function, giving new insights into its behaviour, and was accompanied by publication of the software GL(n)pack as part of D. Goldfeld's book, Automorphic Forms and L-Functions for the Group GL(n,R). Professor Broughan has published widely on problems in prime number theory. His other achievements include co-establishing the New Zealand Mathematical Society, the School of Computing and Mathematical Sciences at the University of Waikato, and the basis for New Zealand's connection to the internet.