The Riemann Hypothesis for Function Fields

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Opis: The Riemann Hypothesis for Function Fields - Machiel van Frankenhuijsen

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.List of illustrations; Preface; Introduction; 1. Valuations; 2. The local theory; 3. The zeta function; 4. Weil positivity; 5. The Frobenius flow; 6. Shift operators; 7. Epilogue; References; Notation; Index.


Szczegóły: The Riemann Hypothesis for Function Fields - Machiel van Frankenhuijsen

Tytuł: The Riemann Hypothesis for Function Fields
Autor: Machiel van Frankenhuijsen
Producent: Cambridge University Press
ISBN: 9781107047211
Rok produkcji: 2014
Ilość stron: 165
Oprawa: Twarda


Recenzje: The Riemann Hypothesis for Function Fields - Machiel van Frankenhuijsen

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The Riemann Hypothesis for Function Fields

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.List of illustrations; Preface; Introduction; 1. Valuations; 2. The local theory; 3. The zeta function; 4. Weil positivity; 5. The Frobenius flow; 6. Shift operators; 7. Epilogue; References; Notation; Index.

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Cena 264,72 PLN
Nasza cena 256,52 PLN
Oszczędzasz 3%
Wysyłka: Niedostępna
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Szczegóły: The Riemann Hypothesis for Function Fields - Machiel van Frankenhuijsen

Tytuł: The Riemann Hypothesis for Function Fields
Autor: Machiel van Frankenhuijsen
Producent: Cambridge University Press
ISBN: 9781107047211
Rok produkcji: 2014
Ilość stron: 165
Oprawa: Twarda


Recenzje: The Riemann Hypothesis for Function Fields - Machiel van Frankenhuijsen

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