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Riemann Hypothesis for Function Fields

Name: Riemann Hypothesis for Function Fields
Brand: Cambridge University Press
SKU: 02051131
Price: 159.49 EUR
Availability: InStock
Author: Machiel van Frankenhuijsen
ISBN: 9781107047211

Frobenius Flow and Shift Operators

Machiel van Frankenhuijsen

Lingua

Inglese

Libro Rigido

Codice Libristo: 02051131

Casa editrice Cambridge University Press, gennaio 2014

This book provides a lucid exposition of the connections between non-commutative geometry and the fa... Descrizione completa

Codice Libristo: 02051131

390 b

159.49 €

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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.