{"product_id":"the-bloch-kato-conjecture-for-the-riemann-zeta-function-paperback-9781107492967","title":"The Bloch–Kato Conjecture for the Riemann Zeta Function (Paperback \/ softback) 9781107492967","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Bloch–Kato Conjecture for the Riemann Zeta Function\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA graduate-level account of an important recent result concerning the Riemann zeta function.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJohn Coates (Edited by), A. Raghuram (Edited by), Anupam Saikia (Edited by), R. Sujatha (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107492967, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 13 March 2015\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e320 pages\u003cbr\u003e22.8 x 15.3 x 1.8 cm, 0.46 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThere 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eList of contributors\u003cbr\u003e Preface A. Raghuram\u003cbr\u003e 1. Special values of the Riemann zeta function: some results and conjectures A. Raghuram\u003cbr\u003e 2. K-theoretic background R. Sujatha\u003cbr\u003e 3. Values of the Riemann zeta function at the odd positive integers and Iwasawa theory John Coates\u003cbr\u003e 4. Explicit reciprocity law of Bloch–Kato and exponential maps Anupam Saikia\u003cbr\u003e 5. The norm residue theorem and the Quillen–Lichtenbaum conjecture Manfred Kolster\u003cbr\u003e 6. Regulators and zeta functions Stephen Lichtenbaum\u003cbr\u003e 7. Soulé's theorem Stephen Lichtenbaum\u003cbr\u003e 8. Soulé's regulator map Ralph Greenberg\u003cbr\u003e 9. On the determinantal approach to the Tamagawa number conjecture T. Nguyen Quang Do\u003cbr\u003e 10. Motivic polylogarithm and related classes Don Blasius\u003cbr\u003e 11. The comparison theorem for the Soulé–Deligne classes Annette Huber\u003cbr\u003e 12. Eisenstein classes, elliptic Soulé elements and the ?-adic elliptic polylogarithm Guido Kings\u003cbr\u003e 13. Postscript R. Sujatha.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Number theory [\u003ca title=\"See our other books on Number theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Number%20theory%20%5BPBH%5D%22\"\u003ePBH\u003c\/a\u003e], Algebra [\u003ca title=\"See our other books on Algebra\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algebra%20%5BPBF%5D%22\"\u003ePBF\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46005361738008,"sku":"9781107492967","price":52.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781107492967i.jpg?v=1696754721","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-bloch-kato-conjecture-for-the-riemann-zeta-function-paperback-9781107492967","provider":"Freshly Printed Books","version":"1.0","type":"link"}