THE RIEMANN HYPOTHESIS FOR FUNCTION FIELDS by Machiel van Frankenhuijsen ( 9781107685314 )

Item Details

Title:

THE RIEMANN HYPOTHESIS FOR FUNCTION FIELDS
FROBENIUS FLOW AND SHIFT OPERATORS

By:

Machiel van Frankenhuijsen

Format:

Paperback

List price:

£38.00

Our price:

£34.20

Discount:

10% off

You save:

£3.80

ISBN 10:

1107685311

ISBN 13:

9781107685314

Availability:

Usually dispatched within 1-3 weeks.

Delivery rates

Stock:

Currently 0 available

Publisher:

CAMBRIDGE UNIVERSITY PRESS

Pub. date:

9 January, 2014

Series:

London Mathematical Society Student Texts 80

Pages:

162

Description:

An exposition of the theory of curves over a finite field, and connections to the Riemann Hypothesis for function fields.

Synopsis:

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.

Illustrations:

12 b/w illus. 1 table

Publication:

Imprint:

Cambridge University Press

Returns:

Returnable

Some other items by this author:

FRACTAL GEOMETRY AND APPLICATIONS (HB)