Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents
(Sprache: Englisch)
This second volume of two presents analytic equivalents to the Riemann hypothesis. Includes an extensive set of appendices.
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This second volume of two presents analytic equivalents to the Riemann hypothesis. Includes an extensive set of appendices.
Klappentext zu „Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents “
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.
Inhaltsverzeichnis zu „Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents “
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.
Bibliographische Angaben
- Autor: Kevin Broughan
- 2017, 522 Seiten, Maße: 24,1 cm, Gebunden, Englisch
- Verlag: Cambridge University Press
- ISBN-10: 1107197120
- ISBN-13: 9781107197121
Sprache:
Englisch
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