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

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Riemann hypothesis for function fields :/ Machiel van Frankenhuijsen, Utah Valley University.
其他題名:	Frobenius flow and shift operators /
作者:	Van Frankenhuysen, Machiel,
面頁冊數:	1 online resource (xii, 152 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Algebraic fields. -
電子資源:	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:

672441
Algebraic fields.

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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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.
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