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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 /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The Riemann hypothesis for function fields/ Machiel van Frankenhuijsen.
其他題名:	Frobenius flow and shift operators /
作者:	Van Frankenhuijsen, Machiel,
出版者:	Cambridge :Cambridge University Press, : 2014.,
面頁冊數:	xii, 152 p. :ill., digital ;24 cm.
標題:	Riemann hypothesis. -
電子資源:	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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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.
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