The Riemann Hypothesis for Function Fields

Frobenius Flow and Shift Operators

Nonfiction, Science & Nature, Mathematics, Number Theory, Geometry
Cover of the book The Riemann Hypothesis for Function Fields by Machiel van Frankenhuijsen, Cambridge University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Machiel van Frankenhuijsen ISBN: 9781107721081
Publisher: Cambridge University Press Publication: January 9, 2014
Imprint: Cambridge University Press Language: English
Author: Machiel van Frankenhuijsen
ISBN: 9781107721081
Publisher: Cambridge University Press
Publication: January 9, 2014
Imprint: Cambridge University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Cambridge University Press

Cover of the book A History of Early Modern Southeast Asia, 1400–1830 by Machiel van Frankenhuijsen
Cover of the book Class in Archaic Greece by Machiel van Frankenhuijsen
Cover of the book Colloidal Suspension Rheology by Machiel van Frankenhuijsen
Cover of the book An Economic Theory of Greed, Love, Groups, and Networks by Machiel van Frankenhuijsen
Cover of the book The Linguistic Past in Twelfth-Century Britain by Machiel van Frankenhuijsen
Cover of the book The Cement of Civil Society by Machiel van Frankenhuijsen
Cover of the book The Cambridge Companion to George Bernard Shaw by Machiel van Frankenhuijsen
Cover of the book Sport, Democracy and War in Classical Athens by Machiel van Frankenhuijsen
Cover of the book The Cambridge Companion to the Poetry of the First World War by Machiel van Frankenhuijsen
Cover of the book Worker Absenteeism and Sick Pay by Machiel van Frankenhuijsen
Cover of the book Learning to Fight by Machiel van Frankenhuijsen
Cover of the book International Law in a Transcivilizational World by Machiel van Frankenhuijsen
Cover of the book A Most Masculine State by Machiel van Frankenhuijsen
Cover of the book 2D Materials by Machiel van Frankenhuijsen
Cover of the book Marine Ecosystems by Machiel van Frankenhuijsen
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy