Read more
On April 25-27, 1989, over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory. The occa sion marked the seventieth birthday and impending (official) retirement of Paul T. Bateman, a prominent number theorist and member of the mathe matics faculty at the University of Illinois for almost forty years. For fifteen of these years, he served as head of the mathematics department. The conference featured a total of fifty-four talks, including ten in vited lectures by H. Delange, P. Erdos, H. Iwaniec, M. Knopp, M. Mendes France, H. L. Montgomery, C. Pomerance, W. Schmidt, H. Stark, and R. C. Vaughan. This volume represents the contents of thirty of these talks as well as two further contributions. The papers span a wide range of topics in number theory, with a majority in analytic number theory.
List of contents
q-Trinomial Coefficients and Rogers-Ramanujan Identities.- Evaluations of Selberg Character Sums.- Oscillations of Quadratic L-Functions.- Elementary Proof of a Theorem of Bateman.- The Prime k-Tuplets Conjecture on Average.- On Arithmetic Functions Involving Consecutive Divisors.- Small Zeros of Quadratic Forms Modulo p, II.- Zeros of Derivatives of the Riemann Zeta-Function near the Critical Line.- On some Exponential Sums.- On the Integers n for which ?(n) = k.- A Boundary Problem for a Pair of Differential-Delay Equations related to Sieve Theory, I.- Some Remarks about Multiplicative Functions of Modulus 1.- On the Normal Behavior of the Iterates of some Arithmetic Functions.- On the Number ofPartitions of n without a Given Subsum, II.- On Gaps between SquarefreeNumbers.- Some Arithmetical Semigroups.- Norms in Arithmetic Progressions.- Lower Bounds for Least Quadratic Non-Residues.- Some Conjectures in Analytic Number Theory and their Connection with Fermat's Last Theorem.- Modular Integrals and their Mellin Transforms.- A Congruence for Generalized Frobenius Partitions with 3 Colors Modulo Powers of 3.- The Coefficients of Cyclotomic Polynomials.- The Rudin-Shapiro Sequence, Ising Chain, and Paperfolding.- On Binomial Equations over Function Fields and a Conjecture of Siegel.- Best Possible Results on the Density of Sumsets.- Some Powers of the Euler Product.- A Divergent Argument Concerning Hadamard Roots of Rational Functions.- Diagonalizing Eisenstein Series. I.- Some Binary Partition Functions.- On the Minimal Level of Modular Forms.- Inequalities for Heights of Algebraic Subspaces and the Thue-Siegel Principle.- The Abstract Prime Number Theorem for Algebraic Function Fields.
