Spectral theory of the Riemann zeta-function:
The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques an...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1997
|
| Schriftenreihe: | Cambridge tracts in mathematics
127 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately |
| Beschreibung: | 1 Online-Ressource (ix, 228 Seiten) |
| ISBN: | 9780511983399 |
| DOI: | 10.1017/CBO9780511983399 |
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| 520 | |a The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately | ||
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Datensatz im Suchindex
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| author | Motohashi, Yoichi 1944- |
| author_GND | (DE-588)11030764X |
| author_facet | Motohashi, Yoichi 1944- |
| author_role | aut |
| author_sort | Motohashi, Yoichi 1944- |
| author_variant | y m ym |
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| bvnumber | BV043942180 |
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| contents | Convention and assumed background -- 1. Non-Euclidean harmonics -- 2. Trace formulas -- 3. Automorphic L-functions -- 4. An explicit formula -- 5. Asymptotics |
| ctrlnum | (ZDB-20-CBO)CR9780511983399 (OCoLC)859642928 (DE-599)BVBBV043942180 |
| dewey-full | 512/.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.73 |
| dewey-search | 512/.73 |
| dewey-sort | 3512 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511983399 |
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| id | DE-604.BV043942180 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511983399 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351149 |
| oclc_num | 859642928 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (ix, 228 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 1997 |
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| spelling | Motohashi, Yoichi 1944- Verfasser (DE-588)11030764X aut Spectral theory of the Riemann zeta-function Yoichi Motohashi Cambridge Cambridge University Press 1997 1 Online-Ressource (ix, 228 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 127 Convention and assumed background -- 1. Non-Euclidean harmonics -- 2. Trace formulas -- 3. Automorphic L-functions -- 4. An explicit formula -- 5. Asymptotics The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately Functions, Zeta Spectral theory (Mathematics) Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Zetafunktion (DE-588)4190764-4 gnd rswk-swf Zetafunktion (DE-588)4190764-4 s Spektraltheorie (DE-588)4116561-5 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-44520-7 Erscheint auch als Druck-Ausgabe 978-0-521-05807-0 https://doi.org/10.1017/CBO9780511983399 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Motohashi, Yoichi 1944- Spectral theory of the Riemann zeta-function Convention and assumed background -- 1. Non-Euclidean harmonics -- 2. Trace formulas -- 3. Automorphic L-functions -- 4. An explicit formula -- 5. Asymptotics Functions, Zeta Spectral theory (Mathematics) Spektraltheorie (DE-588)4116561-5 gnd Zetafunktion (DE-588)4190764-4 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4190764-4 |
| title | Spectral theory of the Riemann zeta-function |
| title_auth | Spectral theory of the Riemann zeta-function |
| title_exact_search | Spectral theory of the Riemann zeta-function |
| title_full | Spectral theory of the Riemann zeta-function Yoichi Motohashi |
| title_fullStr | Spectral theory of the Riemann zeta-function Yoichi Motohashi |
| title_full_unstemmed | Spectral theory of the Riemann zeta-function Yoichi Motohashi |
| title_short | Spectral theory of the Riemann zeta-function |
| title_sort | spectral theory of the riemann zeta function |
| topic | Functions, Zeta Spectral theory (Mathematics) Spektraltheorie (DE-588)4116561-5 gnd Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Functions, Zeta Spectral theory (Mathematics) Spektraltheorie Zetafunktion |
| url | https://doi.org/10.1017/CBO9780511983399 |
| work_keys_str_mv | AT motohashiyoichi spectraltheoryoftheriemannzetafunction |