Random matrices, Frobenius eigenvalues, and monodromy
Author(s)
Bibliographic Information
Random matrices, Frobenius eigenvalues, and monodromy
（Colloquium publications / American Mathematical Society, v. 45）
American Mathematical Society, c1999
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC21:510/K1592070456593
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Note
Includes bibliographical references (p. 417-419)
Description and Table of Contents
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 infinity and related techniques from orthogonal polynomials and Fredholm determinants.
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.
by "Nielsen BookData"