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Colloquium Publications 1999; 419 pp; hardcover Volume: 45 ISBN10: 0821810170 ISBN13: 9780821810170 List Price: US$89 Member Price: US$71.20 Order Code: COLL/45 See also: Eigenvalue Distribution of Large Random Matrices  Leonid Pastur and Mariya Shcherbina Random Matrix Theory: Invariant Ensembles and Universality  Percy Deift and Dimitri Gioev  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 MontgomeryOdlyzko 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. To view the Index, click on the PDF or PostScript file above. Readership Research mathematicians and graduate students interested in varieties over finite and local fields, zetafunctions, limit theorems and structure of families. Reviews "[F]or research workers interested in the Riemann Hypothesis, or in the arithmetic of varieties over finite fields, this work has important messages which may help to shape our thinking on fundamental issues on the nature of zetafunctions."  Bulletin of the London Mathematical Society Table of Contents



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