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 Advanced Studies in Pure Mathematics 2007; 558 pp; hardcover Volume: 49 ISBN-10: 4-931469-43-4 ISBN-13: 978-4-931469-43-3 List Price: US$90 Member Price: US$72 Order Code: ASPM/49 This volume is the proceedings of the International Conference on Probability and Number Theory held at Kanazawa, Japan, in June 2005 and includes several survey articles on probabilistic number theory and research papers on various recent topics around the border area between probability theory and number theory. This volume is useful for all researchers and graduate students who are interested in probability theory and number theory. Volumes in this series are freely available electronically 5 years post-publication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership Graduate students and research mathematicians interested in number theory and probability. Table of Contents B. Adamczewski and Y. Bugeaud -- On the Littlewood conjecture in fields of power series K. Alladi and A. Berkovich -- Series and polynomial representations for weighted Rogers-Ramanujan partitions and products modulo G. J. Babu, E. Manstavicius, and V. Zacharovas -- Limiting processes with dependent increments for measures on symmetric group of permutations P. Elliott -- The ramifications of a shift by 2 K. Fukuyama -- On lacunary trigonometric product R. Garunkštis -- On the Backlund equivalent for the Lindelöf hypothesis P. Hellekalek and P. Liardet -- The dynamics associated with certain digital sequences K.-H. Indlekofer -- New approach to probabilistic number theory--compactifications and integration S. Ito and S.-I. Yasutomi -- On simultaneous Diophantine approximation to periodic points related to modified Jacobi-Perron algorithm A. Laurinčikas -- Limit theorems for the Mellin transform of $$\left\vert\zeta(1/2 +it)\right\vert^2$$. II K. Matsumoto -- On the speed of convergence to limit distributions for Dedekind zeta-functions of non-Galois number fields J.-L. Mauclaire -- On $$\bold Q$$-multiplicative functions having a positive upper-meanvalue M. Mori -- Low discrepancy sequences generated by dynamical systems T. Morita -- Renormalized Rauzy inductions H. Nagoshi -- The universality of $$L$$-functions attached to Maass forms Y. Ohkubo -- The diaphony of a class of infinite sequences J. Pintz -- Approximations to the Goldbach and twin prime problem and gaps between consecutive primes W. Schwarz -- Some highlights from the history of probabilistic number theory R. Šleževičiené-Steuding and J. Steuding -- Gaps between consecutive zeros of the zeta-function on the critical line and conjectures from random matrix theory B. Solomyak -- Eigenfunctions for substitution tiling systems H. Sugita and S. Takanobu -- The probability of two $$\mathbb{F}_q$$-polynomials to be coprime M. Suzuki -- An analogue of the Chowla-Selberg formula for several automorphic $$L$$-functions N. Ushiroya -- On a mean value of a multiplicative function of two variables R. Winkler -- Hartman sets, functions and sequences--a survey Y. Yamasaki -- Integral representations of $$q$$-analogues of the Barnes multiple zeta functions