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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.
Nicholas M. Katz, Princeton University, NJ.Peter Sarnak, Princeton University, NJ
Statements of the main resultsReformulation of the main resultsReduction steps in proving the main theoremsTest functionsHaar measureTail estimatesLarge $N$ limits and Fredholm determinantsSeveral variablesEquidistributionMonodromy of families of curvesMonodromy of some other familiesGUE discrepancies in various familiesDistribution of low-lying Frobenius eigenvalues in various familiesAppendix AD: DensitiesAppendix AG: GraphsReferences.
Henrietta L. Moore, Riverside) Moore, Henrietta L. (London School of Economics and Political Science and University of California, Henrietta Moore, Henrietta L Moore, Henrietta L. Moore