Random matrices, Frobenius eigenvalues, and monodromy / Nicholas M. Katz, Peter Sarnak

... This book is fascinating in many aspects: First, its rigorous, systematic and accessible exposition of the subject makes it a bright landmark at the crossroads of arithmetic and mathematical physics; no doubt it will become a basic reference in random matrix theory. Second, it offers its reader a bouquet of beautiful new results but also leaves the door open to many challenging conjectures ... (MSN)

Bibliogr. p. 417-419. Index

The first two sentences of the preface describe the goals of the authors: “This book shows the scope of analytic number theory in classical and modern directions. There are no division lines; in fact our intent is to demonstrate, particularly for newcomers, the fascinating countless interrelations." Compared with some more or less recent monographs on various branches of analytic number theory such as the zeta- and L-functions with applications to the distribution of primes, exponential and character sums, sieve methods, automorphic functions with spectral theory, Diophantine problems, the circle method, and so on, the range of topics in this comprehensive volume is remarkably wide. Indeed, all the topics mentioned above are covered, among others. There are 26 chapters starting from “Arithmetic Functions" and ending with “Central Values of L-functions". ... (Zentralblatt)