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Riemann Hypothesis for Function Fields

Frobenius Flow and Shift Operators

Language EnglishEnglish
Book Paperback
Book Riemann Hypothesis for Function Fields Machiel van Frankenhuijsen
Libristo code: 02053420
Publishers Cambridge University Press, January 2014
This book provides a lucid exposition of the connections between non-commutative geometry and the fa... Full description
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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.

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About the book

Full name Riemann Hypothesis for Function Fields
Language English
Binding Book - Paperback
Date of issue 2014
Number of pages 162
EAN 9781107685314
ISBN 1107685311
Libristo code 02053420
Weight 260
Dimensions 226 x 153 x 9
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