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OverviewThis 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. Full Product DetailsAuthor: Machiel van Frankenhuijsen (Utah Valley University)Publisher: Cambridge University Press Imprint: Cambridge University Press Volume: 80 Dimensions: Width: 15.20cm , Height: 1.00cm , Length: 22.80cm Weight: 0.260kg ISBN: 9781107685314ISBN 10: 1107685311 Pages: 162 Publication Date: 09 January 2014 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand ![]() We will order this item for you from a manufactured on demand supplier. Table of ContentsReviews'This charming book is an attempt to understand some modern approaches to the [Riemann Hypothesis] ... This intriguing material is recommended, e.g. for an advanced student seminar.' Nieuw Archief voor Wiskunde Author InformationMachiel van Frankenhuijsen is an Associate Professor at Utah Valley University. His research interests lie in number theory, especially the abc conjecture and the connections between geometry and number theory. Tab Content 6Author Website:Countries AvailableAll regions |