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Riemann Hypothesis for Function Fields

Name: Riemann Hypothesis for Function Fields
Brand: Cambridge University Press
SKU: 02053420
Price: 52.52 EUR
Availability: InStock
Author: Machiel van Frankenhuijsen
ISBN: 9781107685314

Frobenius Flow and Shift Operators

Machiel van Frankenhuijsen

Jezik

Angleščina

Knjiga Mehka

Koda Libristo: 02053420

Založba Cambridge University Press, januar 2014

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

Koda Libristo: 02053420

128 b

52.52 €

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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.