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 Negation in Early English by Machiel van Frankenhuijsen
Cover of the book The Cambridge Companion to Comparative Family Law by Machiel van Frankenhuijsen
Cover of the book Politics beyond Black and White by Machiel van Frankenhuijsen
Cover of the book Public Health by Machiel van Frankenhuijsen
Cover of the book Kierkegaard's Fear and Trembling by Machiel van Frankenhuijsen
Cover of the book Atiyah's Accidents, Compensation and the Law by Machiel van Frankenhuijsen
Cover of the book Parliamentary Bills of Rights by Machiel van Frankenhuijsen
Cover of the book Poetic Ethics in Proverbs by Machiel van Frankenhuijsen
Cover of the book Rome and the Making of a World State, 150 BCE–20 CE by Machiel van Frankenhuijsen
Cover of the book Constitution Making during State Building by Machiel van Frankenhuijsen
Cover of the book First Language Acquisition by Machiel van Frankenhuijsen
Cover of the book Popular Sovereignty in Historical Perspective by Machiel van Frankenhuijsen
Cover of the book French Liberalism from Montesquieu to the Present Day by Machiel van Frankenhuijsen
Cover of the book The Manufacturing of Markets by Machiel van Frankenhuijsen
Cover of the book Archaeology and the Senses 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