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The Riemann hypothesis for function ...

Van Frankenhuijsen, Machiel, (1967-)

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The Riemann hypothesis for function fields = Frobenius flow and shift operators /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Riemann hypothesis for function fields/ Machiel van Frankenhuijsen.
Reminder of title:	Frobenius flow and shift operators /
Author:	Van Frankenhuijsen, Machiel,
Published:	Cambridge :Cambridge University Press, : 2014.,
Description:	xii, 152 p. :ill., digital ;24 cm.
Subject:	Riemann hypothesis. -
Online resource:	https://doi.org/10.1017/CBO9781107238992
ISBN:	9781107238992

The Riemann hypothesis for function fields = Frobenius flow and shift operators /
Van Frankenhuijsen, Machiel,1967-

The Riemann hypothesis for function fieldsFrobenius flow and shift operators /[electronic resource] :Machiel van Frankenhuijsen. - Cambridge :Cambridge University Press,2014. - xii, 152 p. :ill., digital ;24 cm. - London Mathematical Society student texts ;80. - 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.

ISBN: 9781107238992Subjects--Topical Terms:

3259151
Riemann hypothesis.

LC Class. No.: QA246 / .V36 2014

Dewey Class. No.: 512.73

The Riemann hypothesis for function fields = Frobenius flow and shift operators /
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245 1 4 $a The Riemann hypothesis for function fields $h [electronic resource] : $b Frobenius flow and shift operators / $c Machiel van Frankenhuijsen.
260 $a Cambridge : $b Cambridge University Press, $c 2014.
300 $a xii, 152 p. : $b ill., digital ; $c 24 cm.
490 1 $a London Mathematical Society student texts ; $v 80
520 $a 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.
650 0 $a Riemann hypothesis. $3 3259151
650 0 $a Noncommutative differential geometry. $3 629838
650 0 $a Algebraic fields. $3 532032
830 0 $a London Mathematical Society student texts ; $v 80. $3 3391869
856 4 0 $u https://doi.org/10.1017/CBO9781107238992