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Equivalents of the Riemann hypothesis. volume 2 : Analytic Equivalents

Author: Kevin A Broughan
Publisher: Cambridge : Cambridge University Press, 2017.
Series: Encyclopedia of mathematics and its applications, 165.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Kevin A Broughan
ISBN: 9781108178266 110817826X
OCLC Number: 1009077507
Description: 1 online resource.
Contents: 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.
Series Title: Encyclopedia of mathematics and its applications, 165.
Responsibility: Kevin Broughan.

Abstract:

This two-volume work presents the main known equivalents to the Riemann hypothesis, perhaps the most important problem in mathematics. Volume 2 covers equivalents with a strong analytic orientation  Read more...

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'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 Read more...

 
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