The Bloch-Kato conjecture for the Riemann zeta function:
There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that the...
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| Other Authors: | , , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2015
|
| Series: | London Mathematical Society lecture note series
418 |
| Subjects: | |
| Links: | https://doi.org/10.1017/CBO9781316163757 https://doi.org/10.1017/CBO9781316163757 https://doi.org/10.1017/CBO9781316163757 |
| Summary: | There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that these values are related to the higher K-theory of the ring of integers. Shortly afterwards, Bloch and Kato proposed a Tamagawa number-type conjecture for these values, and showed that it would follow from a result in motivic cohomology which was unknown at the time. This vital result from motivic cohomology was subsequently proven by Huber, Kings, and Wildeshaus. Bringing together key results from K-theory, motivic cohomology, and Iwasawa theory, this book is the first to give a complete proof, accessible to graduate students, of the Bloch–Kato conjecture for odd positive integers. It includes a new account of the results from motivic cohomology by Huber and Kings |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (ix, 305 pages) |
| ISBN: | 9781316163757 |
| DOI: | 10.1017/CBO9781316163757 |
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| spelling | The Bloch-Kato conjecture for the Riemann zeta function edited by John Coates, A. Raghuram, Anupan Saikia, R. Sujatha Cambridge Cambridge University Press 2015 1 online resource (ix, 305 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 418 Title from publisher's bibliographic system (viewed on 05 Oct 2015) There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that these values are related to the higher K-theory of the ring of integers. Shortly afterwards, Bloch and Kato proposed a Tamagawa number-type conjecture for these values, and showed that it would follow from a result in motivic cohomology which was unknown at the time. This vital result from motivic cohomology was subsequently proven by Huber, Kings, and Wildeshaus. Bringing together key results from K-theory, motivic cohomology, and Iwasawa theory, this book is the first to give a complete proof, accessible to graduate students, of the Bloch–Kato conjecture for odd positive integers. It includes a new account of the results from motivic cohomology by Huber and Kings Functions, Zeta / Congresses Riemann hypothesis / Congresses L-functions / Congresses Motives (Mathematics) / Congresses Iwasawa theory / Congresses K-theory / Congresses Galois cohomology / Congresses Riemannsche Zetafunktion (DE-588)4308419-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Riemannsche Zetafunktion (DE-588)4308419-9 s 1\p DE-604 Coates, J. edt Raghuram, A. edt Saikia, Anupam edt Sujatha, R. edt Erscheint auch als Druckausgabe 978-1-107-49296-7 https://doi.org/10.1017/CBO9781316163757 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | The Bloch-Kato conjecture for the Riemann zeta function Functions, Zeta / Congresses Riemann hypothesis / Congresses L-functions / Congresses Motives (Mathematics) / Congresses Iwasawa theory / Congresses K-theory / Congresses Galois cohomology / Congresses Riemannsche Zetafunktion (DE-588)4308419-9 gnd |
| subject_GND | (DE-588)4308419-9 (DE-588)1071861417 |
| title | The Bloch-Kato conjecture for the Riemann zeta function |
| title_auth | The Bloch-Kato conjecture for the Riemann zeta function |
| title_exact_search | The Bloch-Kato conjecture for the Riemann zeta function |
| title_full | The Bloch-Kato conjecture for the Riemann zeta function edited by John Coates, A. Raghuram, Anupan Saikia, R. Sujatha |
| title_fullStr | The Bloch-Kato conjecture for the Riemann zeta function edited by John Coates, A. Raghuram, Anupan Saikia, R. Sujatha |
| title_full_unstemmed | The Bloch-Kato conjecture for the Riemann zeta function edited by John Coates, A. Raghuram, Anupan Saikia, R. Sujatha |
| title_short | The Bloch-Kato conjecture for the Riemann zeta function |
| title_sort | the bloch kato conjecture for the riemann zeta function |
| topic | Functions, Zeta / Congresses Riemann hypothesis / Congresses L-functions / Congresses Motives (Mathematics) / Congresses Iwasawa theory / Congresses K-theory / Congresses Galois cohomology / Congresses Riemannsche Zetafunktion (DE-588)4308419-9 gnd |
| topic_facet | Functions, Zeta / Congresses Riemann hypothesis / Congresses L-functions / Congresses Motives (Mathematics) / Congresses Iwasawa theory / Congresses K-theory / Congresses Galois cohomology / Congresses Riemannsche Zetafunktion Konferenzschrift |
| url | https://doi.org/10.1017/CBO9781316163757 |
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