Equivalents of the Riemann Hypothesis: Volume 3 Further steps towards resolving the Riemann Hypothesis
The Riemann hypothesis (RH) may be the most important outstanding problem in mathematics. This third volume on equivalents to RH comprehensively presents recent results of Nicolas, Rogers-Tao-Dobner, Polymath15, and Matiyasevich. Particularly interesting are derivations which show, assuming all zero...
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| Format: | eBook |
| Language: | English |
| Published: |
Cambridge, England
Cambridge University Press
2024
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| Series: | Encyclopedia of mathematics and its applications
187 |
| Links: | https://doi.org/10.1017/9781009384780 |
| Summary: | The Riemann hypothesis (RH) may be the most important outstanding problem in mathematics. This third volume on equivalents to RH comprehensively presents recent results of Nicolas, Rogers-Tao-Dobner, Polymath15, and Matiyasevich. Particularly interesting are derivations which show, assuming all zeros on the critical line are simple, that RH is decidable. Also included are classical Pólya-Jensen equivalence and related developments of Ono et al. Extensive appendices highlight key background results, most of which are proved. The book is highly accessible, with definitions repeated, proofs split logically, and graphical visuals. It is ideal for mathematicians wishing to update their knowledge, logicians, and graduate students seeking accessible number theory research problems. The three volumes can be read mostly independently. Volume 1 presents classical and modern arithmetic RH equivalents. Volume 2 covers equivalences with a strong analytic orientation. Volume 3 includes further arithmetic and analytic equivalents plus new material on RH decidability. |
| Physical Description: | 1 Online-Ressource (xx, 684 Seiten) |
| ISBN: | 9781009384780 |
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| spelling | Broughan, Kevin A. 1943- Equivalents of the Riemann Hypothesis Volume 3 Further steps towards resolving the Riemann Hypothesis Kevin Broughan Cambridge, England Cambridge University Press 2024 1 Online-Ressource (xx, 684 Seiten) txt c cr Encyclopedia of mathematics and its applications 187 The Riemann hypothesis (RH) may be the most important outstanding problem in mathematics. This third volume on equivalents to RH comprehensively presents recent results of Nicolas, Rogers-Tao-Dobner, Polymath15, and Matiyasevich. Particularly interesting are derivations which show, assuming all zeros on the critical line are simple, that RH is decidable. Also included are classical Pólya-Jensen equivalence and related developments of Ono et al. Extensive appendices highlight key background results, most of which are proved. The book is highly accessible, with definitions repeated, proofs split logically, and graphical visuals. It is ideal for mathematicians wishing to update their knowledge, logicians, and graduate students seeking accessible number theory research problems. The three volumes can be read mostly independently. Volume 1 presents classical and modern arithmetic RH equivalents. Volume 2 covers equivalences with a strong analytic orientation. Volume 3 includes further arithmetic and analytic equivalents plus new material on RH decidability. Erscheint auch als Druck-Ausgabe 9781009384803 |
| spellingShingle | Broughan, Kevin A. 1943- Equivalents of the Riemann Hypothesis |
| title | Equivalents of the Riemann Hypothesis |
| title_auth | Equivalents of the Riemann Hypothesis |
| title_exact_search | Equivalents of the Riemann Hypothesis |
| title_full | Equivalents of the Riemann Hypothesis Volume 3 Further steps towards resolving the Riemann Hypothesis Kevin Broughan |
| title_fullStr | Equivalents of the Riemann Hypothesis Volume 3 Further steps towards resolving the Riemann Hypothesis Kevin Broughan |
| title_full_unstemmed | Equivalents of the Riemann Hypothesis Volume 3 Further steps towards resolving the Riemann Hypothesis Kevin Broughan |
| title_short | Equivalents of the Riemann Hypothesis |
| title_sort | equivalents of the riemann hypothesis further steps towards resolving the riemann hypothesis |
| work_keys_str_mv | AT broughankevina equivalentsoftheriemannhypothesisvolume3 |