Analytic Number Theory

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.