Equivalents of the Riemann Hypothesis

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Sprache: Englisch

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Beschreibung

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

Über den Autor

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.

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2018
Fachbereich:	Allgemeines
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
ISBN-13:	9781107197121
ISBN-10:	1107197120
Sprache:	Englisch
Ausstattung / Beilage:	HC gerader Rücken kaschiert
Einband:	Gebunden
Autor:	Broughan, Kevin
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	240 x 161 x 34 mm
Von/Mit:	Kevin Broughan
Erscheinungsdatum:	08.01.2018
Gewicht:	1,023 kg

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