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Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents de Kevin Broughan

Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents: Encyclopedia of Mathematics and its Applications, cartea 165

Autor Kevin Broughan
en Limba Engleză Hardback – noi 2017
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.
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Specificații

ISBN-13: 9781107197121
ISBN-10: 1107197120
Pagini: 522
Dimensiuni: 162 x 241 x 32 mm
Greutate: 0.88 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Encyclopedia of Mathematics and its Applications

Locul publicării:New York, United States

Cuprins

1. Introduction; 2. Series equivalents; 3. Banach and Hilbert space methods; 4. The Riemann Xi function; 5. The de Bruijn-Newman constant; 6. Orthogonal polynomials; 7. Cyclotomic polynomials; 8. Integral equations; 9. Weil's explicit formula, inequality and conjectures; 10. Discrete measures; 11. Hermitian forms; 12. Dirichlet L-functions; 13. Smooth numbers; 14. Epilogue; Appendix A. Convergence of series; Appendix B. Complex function theory; Appendix C. The Riemann-Stieltjes integral; Appendix D. The Lebesgue integral on R; Appendix E. Fourier transform; Appendix F. The Laplace transform; Appendix G. The Mellin transform; Appendix H. The gamma function; Appendix I. Riemann Zeta function; Appendix J. Banach and Hilbert spaces; Appendix K. Miscellaneous background results; Appendix L. GRHpack mini-manual; References; Index.

Recenzii

'Throughout the book careful proofs are given for all the results discussed, introducing an impressive range of mathematical tools. Indeed, the main achievement of the work is the way in which it demonstrates how all these diverse subject areas can be brought to bear on the Riemann hypothesis. The exposition is accessible to strong undergraduates, but even specialists will find material here to interest them.' D. R. Heath-Brown, Mathematical Reviews
'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
'The two volumes are a very valuable resource and a fascinating read about a most intriguing problem.' R.S. MacKay, London Mathematical Society Newsletter
'All in all these books serve as a good introduction to a wide range of mathematics related to the Riemann Hypothesis and make for a valuable contribution to the literature. They are truly encyclopedic and I am sure will entice many a reader to consult some literature quoted and who knows, eventually make an own contribution to the area.' Pieter Moree, Nieuw Archief voor Wiskunde
'This book may serve as reference for the Riemann hypothesis and its equivalent formulations or as an inspiration for everyone interested in number theory. It is written in a very readable style and for most parts only assumes basic knowledge from (complex analysis). Thus it may also serve as a (somewhat specific) introduction to analytic number theory.' J. Mahnkopf, Encyclopedia of Mathematics and its Applications

Notă biografică

Descriere

This second volume of two presents analytic equivalents to the Riemann hypothesis. Includes an extensive set of appendices.