The Riemann Hypothesis for Function Fields by Machiel Van Frankenhuijsen
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.-
Hyperbolic Geometry from a Local Viewpoint
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Undergraduate Algebraic Geometry
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The Prime Number Theorem
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Elements of the Representation Theory of Associative Algebras: Volume 2, Tubes and Concealed Algebras of Euclidean type
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Notes on Hamiltonian Dynamical Systems
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LMSST: 24 Lectures on Elliptic Curves
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A Brief Guide to Algebraic Number Theory
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Designs, Graphs, Codes and their Links
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Logic, Induction and Sets
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Fourier Analysis on Finite Groups and Applications
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Introduction to Combinators and (lambda) Calculus
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Representation Theorems in Hardy Spaces
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Introduction to Approximate Groups
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The Block Theory of Finite Group Algebras
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Hyperbolic Geometry
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Random Graphs, Geometry and Asymptotic Structure
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Undergraduate Commutative Algebra
- Nearly Invariant Subspaces and their Applications
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Celestial Mechanics
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Sets and Transfinite Algebra
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The Shrikhande Graph
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Topics in Cyclic Theory
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An Introduction to the Theory of Graph Spectra
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Clifford Algebras: An Introduction
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Introduction to Banach Algebras, Operators, and Harmonic Analysis
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Fast Track to Forcing
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The Block Theory of Finite Group Algebras: Volume 1
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Computational Algebraic Geometry
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Lectures on Kahler Geometry
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Fourier Analysis: Volume 1, Theory
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Semigroups of Linear Operators
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An Introduction to Noncommutative Noetherian Rings
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The Calculus of Braids
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A Gentle Introduction to Homological Mirror Symmetry
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Set Theory
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Tensor Products of C*-Algebras and Operator Spaces
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Introductory Lectures on Rings and Modules
'This charming book is an attempt to understand some modern approaches to the [Riemann Hypothesis] … This intriguing material is recommended, eg. for an advanced student seminar.' Nieuw Archief voor Wiskunde
'This lovely book offers an easy-pace account of the Riemann Hypothesis (RH) for function fields.' Anton Deitmar, Mathematical Reviews
'This lovely book offers an easy-pace account of the Riemann Hypothesis (RH) for function fields.' Anton Deitmar, Mathematical Reviews
Machiel 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.
| SKU | Unavailable |
| ISBN 13 | 9781107047211 |
| ISBN 10 | 1107047218 |
| Title | The Riemann Hypothesis for Function Fields |
| Author | Machiel Van Frankenhuijsen |
| Series | London Mathematical Society Student Texts |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 2014-01-09 |
| Number of pages | 166 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |