The Riemann hypothesis for function fields: Frobenius flow and shift operators
This book provides a lucid exposition of the connections between non-commutative geometry and the famous Riemann Hypothesis, focusing on the theory of one-dimensional varieties over a finite field. The reader will encounter many important aspects of the theory, such as Bombieri's proof of the R...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2014
|
| Series: | London Mathematical Society student texts
80 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | This book provides a lucid exposition of the connections between non-commutative geometry and the famous Riemann Hypothesis, focusing on the theory of one-dimensional varieties over a finite field. The reader will encounter many important aspects of the theory, such as Bombieri's proof of the Riemann Hypothesis for function fields, along with an explanation of the connections with Nevanlinna theory and non-commutative geometry. The connection with non-commutative geometry is given special attention, with a complete determination of the Weil terms in the explicit formula for the point counting function as a trace of a shift operator on the additive space, and a discussion of how to obtain the explicit formula from the action of the idele class group on the space of adele classes. The exposition is accessible at the graduate level and above, and provides a wealth of motivation for further research in this area |
| Physical Description: | 1 Online-Ressource (xii, 152 Seiten) |
| ISBN: | 9781107238992 |
| DOI: | 10.1017/CBO9781107238992 |
Staff View
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| discipline | Mathematik |
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| id | DE-604.BV043940982 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9781107238992 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349951 |
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| spelling | Frankenhuysen, Machiel van 1967- Verfasser (DE-588)12181632X aut The Riemann hypothesis for function fields Frobenius flow and shift operators Machiel van Frankenhuijsen, Utah Valley University Cambridge Cambridge University Press 2014 1 Online-Ressource (xii, 152 Seiten) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society student texts 80 This book provides a lucid exposition of the connections between non-commutative geometry and the famous Riemann Hypothesis, focusing on the theory of one-dimensional varieties over a finite field. The reader will encounter many important aspects of the theory, such as Bombieri's proof of the Riemann Hypothesis for function fields, along with an explanation of the connections with Nevanlinna theory and non-commutative geometry. The connection with non-commutative geometry is given special attention, with a complete determination of the Weil terms in the explicit formula for the point counting function as a trace of a shift operator on the additive space, and a discussion of how to obtain the explicit formula from the action of the idele class group on the space of adele classes. The exposition is accessible at the graduate level and above, and provides a wealth of motivation for further research in this area Riemann hypothesis Noncommutative differential geometry Algebraic fields Riemannsche Vermutung (DE-588)4704537-1 gnd rswk-swf Riemannsche Vermutung (DE-588)4704537-1 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-107-04721-1 Erscheint auch als Druck-Ausgabe 978-1-107-68531-4 https://doi.org/10.1017/CBO9781107238992 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Frankenhuysen, Machiel van 1967- The Riemann hypothesis for function fields Frobenius flow and shift operators Riemann hypothesis Noncommutative differential geometry Algebraic fields Riemannsche Vermutung (DE-588)4704537-1 gnd |
| subject_GND | (DE-588)4704537-1 |
| title | The Riemann hypothesis for function fields Frobenius flow and shift operators |
| title_auth | The Riemann hypothesis for function fields Frobenius flow and shift operators |
| title_exact_search | The Riemann hypothesis for function fields Frobenius flow and shift operators |
| title_full | The Riemann hypothesis for function fields Frobenius flow and shift operators Machiel van Frankenhuijsen, Utah Valley University |
| title_fullStr | The Riemann hypothesis for function fields Frobenius flow and shift operators Machiel van Frankenhuijsen, Utah Valley University |
| title_full_unstemmed | The Riemann hypothesis for function fields Frobenius flow and shift operators Machiel van Frankenhuijsen, Utah Valley University |
| title_short | The Riemann hypothesis for function fields |
| title_sort | the riemann hypothesis for function fields frobenius flow and shift operators |
| title_sub | Frobenius flow and shift operators |
| topic | Riemann hypothesis Noncommutative differential geometry Algebraic fields Riemannsche Vermutung (DE-588)4704537-1 gnd |
| topic_facet | Riemann hypothesis Noncommutative differential geometry Algebraic fields Riemannsche Vermutung |
| url | https://doi.org/10.1017/CBO9781107238992 |
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