On May 16 -20, 1995, approximately 150 mathematicians gathered at the Conference Center of the University of Illinois at Allerton Park for an Inter­ national Conference on Analytic Number Theory. The meeting marked the approaching official retirement of Heini Halberstam from the mathematics fac­ ulty of the University of Illinois at Urbana-Champaign. Professor Halberstam has been at the University since 1980, for 8 years as head of the Department of Mathematics, and has been a leading researcher and teacher in number theory for over forty years. The program included invited one hour lectures by G. Andrews, J. Bour­ gain, J. M. Deshouillers, H. Halberstam, D. R. Heath-Brown, H. Iwaniec, H. L. Montgomery, R. Murty, C. Pomerance, and R. C. Vaughan, and almost one hundred other talks of varying lengths. These volumes comprise contributions from most of the principal speakers and from many of the other participants, as well as some papers from mathematicians who were unable to attend. The contents span a broad range of themes from contemporary number theory, with the majority having an analytic flavor.

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of Volume 1.- Weighted partition identities and applications.- Rogers-Ramanujan polynomials for modulus 6.- On subset-sum-distinct sequences.- The Brun-Titchmarsh Theorem on average.- Congruences for Fourier coefficients of half-integral weight modular forms and special values of L-functions.- The asymptotic formula for the number of representations of an integer as a sum of five squares.- Distribution of the error term for the number of lattice points inside a shifted ball.- A probabilistic generalization of the Riemann zeta function.- A general Heine transformation and symmetric polynomials of Rogers.- A sieve auxiliary function.- Bounds on complete exponential sums.- A note on the fourth power moment of the Riemann zeta-function.- Effective estimates of exponential sums over primes.- On products of multiplicative functions of absolute value at most 1 which are composed with linear functions.- Combinatorial sieves of dimension exceeding one II.- Congruences for partition functions.- Fractional power large sieves.- Some problems I presented or planned to present in my short talk.- On the number of divisors of n!.- Generalized Lambert series.- A generalization of an irreducibility theorem of I. Schur.- Bombieri's sieve.- Bh sequences.