The arithmetic of function fields
The arithmetic of the coefficients of half-integral weight Eisenstein series
The Arithmetic Theory of Local Constants for abelian Varieties
The asymptotic behavior of the average -discrepancies and a randomized discrepancy.
The asymptotic behaviour of the counting functions of Ω-sets in arithmetical semigroups
We consider an axiomatically-defined class of arithmetical semigroups that we call simple L-semigroups. This class includes all generalized Hilbert semigroups, in particular the semigroup of non-zero integers in any algebraic number field. We show, for all positive integers k, that the counting function of the set of elements with at most k distinct factorization lengths in such a semigroup has oscillations of logarithmic frequency and size for some M>0. More generally, we show a result on...
The asymptotic behaviour of the number of solutions of polynomial congruences.
The asymptotic distribution of exponential sums. I.
The asymptotic distribution of exponential sums. II.
The asymptotic distribution of Kloosterman sums
The asymptotic distribution of the number of summands in unrestricted Λ-partitions
The Aubert involution and R-groups
The automorphism group of some semigroups
The average distribution of cubic exponential sums.
The average least witness is 2
The average length of a trajectory in a certain billiard in a flat two-torus.
The average of the least primitive root modulo
The average order of a class of arithmetic functions over arithmetic progressions with applications to quadratic forms.
The average order of a permutation.
The average order of over integers free of large prime factors
The average order of the Dirichlet series of the gcd-sum function.