Analytic Number Theory : Proceedings of a Conference In Honor of Heini Halberstam Volume 1

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. Front Matter....Pages i-xiv Weighted partition identities and applications....Pages 1-15 Rogers-Ramanujan polynomials for modulus 6....Pages 17-30 On subset-sum-distinct sequences....Pages 31-37 The Brun-Titchmarsh Theorem on average....Pages 39-103 Congruences for Fourier coefficients of half-integral weight modular forms and special values of L-functions....Pages 105-128 The asymptotic formula for the number of representations of an integer as a sum of five squares....Pages 129-139 Distribution of the error term for the number of lattice points inside a shifted ball....Pages 141-153 A probabilistic generalization of the Riemann zeta function....Pages 155-162 A general Heine transformation and symmetric polynomials of Rogers....Pages 163-171 A Sieve Auxiliary Function....Pages 173-210 Bounds on complete exponential sums....Pages 211-224 A note on the fourth power moment of the Riemann zeta-function....Pages 225-230 Effective estimates of exponential sums over primes....Pages 231-244 On Products of Multiplicative Functions of Absolute Value at Most 1 Which are Composed with Linear Functions....Pages 245-263 Combinatorial sieves of dimension exceeding one II....Pages 265-308 Congruences for partition functions....Pages 309-321 Fractional power large sieves....Pages 323-332 Some problems I presented or planned to present in my short talk....Pages 333-335 On the number of divisors of n!....Pages 337-355 Generalized Lambert series....Pages 357-370 A generalization of an irreducibility theorem of I. Schur....Pages 371-396 Bombieri’s sieve....Pages 411-430 B h sequences....Pages 431-449 The second of two volumes presenting papers from an international conference on analytic number theory. The two volumes contain 50 papers, with an emphasis on topics such as sieves, related combinatorial aspects, multiplicative number theory, additive number theory, and Riemann zeta-function.