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. The authors draw upon many disparate areas of mathematics from algebraic geometry, moduli spaces, mondromy, equidistribution, and the Weil conjectures to probability theory and the compact classical groups.
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Verlagsort
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ISBN-13
978-1-4704-7507-9 (9781470475079)
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Schweitzer Klassifikation
Nicholas M. Katz, Princeton University, NJ.
Peter Sarnak, Princeton University, NJ
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 AD: Densities
Appendix AG: Graphs
References.
