國立虎尾科技大學 |

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

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The Riemann hypothesis for function fields :/ Machiel van Frankenhuijsen, Utah Valley University.
Reminder of title:	Frobenius flow and shift operators /
Author:	Van Frankenhuysen, Machiel,
Description:	1 online resource (xii, 152 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Riemann hypothesis. -
Online resource:	https://doi.org/10.1017/CBO9781107238992
ISBN:	9781107238992 (ebook)

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

The Riemann hypothesis for function fields :Frobenius flow and shift operators /Machiel van Frankenhuijsen, Utah Valley University. - 1 online resource (xii, 152 pages) :digital, PDF file(s). - London Mathematical Society student texts ;80. - London Mathematical Society student texts ;81..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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: 9781107238992 (ebook)Subjects--Topical Terms:

1201268
Riemann hypothesis.

LC Class. No.: QA246 / .V36 2014

Dewey Class. No.: 512.73

The Riemann hypothesis for function fields : = Frobenius flow and shift operators /
LDR:02047nam a2200301 i 4500 001 1127486
003 UkCbUP
005 20151005020621.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 240926s2014||||enk o ||1 0|eng|d
020 $a 9781107238992 (ebook)
020 $z 9781107047211 (hardback)
020 $z 9781107685314 (paperback)
035 $a CR9781107238992
040 $a UkCbUP $b eng $e rda $c UkCbUP
050 0 0 $a QA246 $b .V36 2014
082 0 0 $a 512.73 $2 23
100 1 $a Van Frankenhuysen, Machiel, $d 1967- $e author. $3 1446914
245 1 4 $a The Riemann hypothesis for function fields : $b Frobenius flow and shift operators / $c Machiel van Frankenhuijsen, Utah Valley University.
264 1 $a Cambridge : $b Cambridge University Press, $c 2014.
300 $a 1 online resource (xii, 152 pages) : $b digital, PDF file(s).
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
490 1 $a London Mathematical Society student texts ; $v 80
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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 1201268
650 0 $a Noncommutative differential geometry. $3 681235
650 0 $a Algebraic fields. $3 672441
776 0 8 $i Print version: $z 9781107047211
830 0 $a London Mathematical Society student texts ; $v 81. $3 1156767
856 4 0 $u https://doi.org/10.1017/CBO9781107238992