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Random Matrices, Frobenius Eigenvalues, and Monodromy

Nicholas M. Katz Princeton University, Princeton, NJ
Peter Sarnak Princeton University, Princeton, NJ
Available Formats:
Hardcover ISBN: 978-0-8218-1017-0
Product Code: COLL/45
List Price: $95.00 MAA Member Price:$85.50
AMS Member Price: $76.00 Electronic ISBN: 978-1-4704-3191-4 Product Code: COLL/45.E List Price:$89.00
MAA Member Price: $80.10 AMS Member Price:$71.20
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List Price: $142.50 MAA Member Price:$128.25
AMS Member Price: $114.00 Click above image for expanded view Random Matrices, Frobenius Eigenvalues, and Monodromy Nicholas M. Katz Princeton University, Princeton, NJ Peter Sarnak Princeton University, Princeton, NJ Available Formats:  Hardcover ISBN: 978-0-8218-1017-0 Product Code: COLL/45  List Price:$95.00 MAA Member Price: $85.50 AMS Member Price:$76.00
 Electronic ISBN: 978-1-4704-3191-4 Product Code: COLL/45.E
 List Price: $89.00 MAA Member Price:$80.10 AMS Member Price: $71.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$142.50 MAA Member Price: $128.25 AMS Member Price:$114.00
• Book Details

Colloquium Publications
Volume: 451999; 419 pp
MSC: 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.

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

• Reviews

• [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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 451999; 419 pp
MSC: 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.

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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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