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| Softcover ISBN: | 978-1-4704-7507-9 |
| Product Code: | COLL/45.S |
| List Price: | $99.00 |
| MAA Member Price: | $89.10 |
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| eBook ISBN: | 978-1-4704-3191-4 |
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| Softcover ISBN: | 978-1-4704-7507-9 |
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Book DetailsColloquium PublicationsVolume: 45; 1999; 419 ppMSC: Primary 11; 14; 60; Secondary 82
The main topic of this book is the deep relation between the spacings between zeros of zeta and \(L\)-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and \(L\)-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants.
To view the Index, click on the PDF or PostScript file above.
ReadershipResearch mathematicians and graduate students interested in varieties over finite and local fields, zeta-functions, limit theorems and structure of families.
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Table of Contents
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Chapters
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Chapter 1. Introduction
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Chapter 2. Statements of the main results
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Chapter 3. Reformulation of the main results
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Chapter 4. Reduction steps in proving the main theorems
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Chapter 5. Test functions
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Chapter 6. Haar measure
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Chapter 7. Tail estimates
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Chapter 8. Large N limits and Fredholm determinants
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Chapter 9. Several variables
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Chapter 10. Equidistribution
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Chapter 11. Monodromy of families of curves
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Chapter 12. Monodromy of some other families
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Chapter 13. GUE discrepancies in various families
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Chapter 14. Distribution of low-lying Frobenius eigenvalues in various families
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Appendix: Densities
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Appendix: Graphs
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Additional Material
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Reviews
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[F]or research workers interested in the Riemann Hypothesis, or in the arithmetic of varieties over finite fields, this work has important messages which may help to shape our thinking on fundamental issues on the nature of zeta-functions.
Bulletin of the London Mathematical Society
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
The main topic of this book is the deep relation between the spacings between zeros of zeta and \(L\)-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and \(L\)-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants.
To view the Index, click on the PDF or PostScript file above.
Research mathematicians and graduate students interested in varieties over finite and local fields, zeta-functions, limit theorems and structure of families.
-
Chapters
-
Chapter 1. Introduction
-
Chapter 2. Statements of the main results
-
Chapter 3. Reformulation of the main results
-
Chapter 4. Reduction steps in proving the main theorems
-
Chapter 5. Test functions
-
Chapter 6. Haar measure
-
Chapter 7. Tail estimates
-
Chapter 8. Large N limits and Fredholm determinants
-
Chapter 9. Several variables
-
Chapter 10. Equidistribution
-
Chapter 11. Monodromy of families of curves
-
Chapter 12. Monodromy of some other families
-
Chapter 13. GUE discrepancies in various families
-
Chapter 14. Distribution of low-lying Frobenius eigenvalues in various families
-
Appendix: Densities
-
Appendix: Graphs
-
[F]or research workers interested in the Riemann Hypothesis, or in the arithmetic of varieties over finite fields, this work has important messages which may help to shape our thinking on fundamental issues on the nature of zeta-functions.
Bulletin of the London Mathematical Society
