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THE RIEMANN HYPOTHESIS FOR FUNCTIONS FIELDS
FRANKENHUIJSEN VAN M. wydawnictwo: CAMBRIDGE UNIVERSITY, 2014, wydanie I cena netto: 310.00 Twoja cena 294,50 zł + 5% vat - dodaj do koszyka The Riemann Hypothesis for Function Fields
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.
List of illustrations; Preface; Introduction;
1. Valuations;
2. The local theory;
3. The zeta function;
4. Weil positivity;
5. The Frobenius flow;
6. Shift operators;
7. Epilogue; References; Notation; Index.
162 pages, Hardcover
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