Description
Book SynopsisThe 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.
Table of Contents
- 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.
