ENGLISH

Random Matrices, Frobenius Eigenvalues, and Monodromy

By Nicholas M. Katz , Peter Sarnak

Book information

Publisher
AMS
Year
1999
ISBN
1470431912, 9781470431914
Language
english
Format
PDF
Filesize
97 MB (101716188 bytes)
Series
Colloquium Publications 45
Pages
427\441
Time added
2023-06-13 08:25:56

Description

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 infinit. Cover Title page Contents Introduction Statements of the main results Reformulation of the main results Reduction steps in proving the main theorems Test functions Haar measure Tail estimates Large N limits and Fredholm determinants Several variables Equidistribution Monodromy of families of curves Monodromy of some other families GUE discrepancies in various families Distribution of low-lying Frobenius eigenvalues in various families Appendix: Densities Appendix: Graphs References Back Cover

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