Asymptotic expansions of finite theta series
Bilinear forms in the Fourier coefficients of half-integral weight cusp forms and sums over primes.
Bioctic Gauss sums and sixteenth power residue difference sets
Caractères quadratiques de groupes abéliens finis et sommes de Gauss
Character sums in complex half-planes
Let be a finite subset of an abelian group and let be a closed half-plane of the complex plane, containing zero. We show that (unless possesses a special, explicitly indicated structure) there exists a non-trivial Fourier coefficient of the indicator function of which belongs to . In other words, there exists a non-trivial character such that .
Computing higher rank primitive root densities
We extend the "character sum method" for the computation of densities in Artin primitive root problems given by Lenstra and the authors to the situation of radical extensions of arbitrary rank. Our algebraic set-up identifies the key parameters of the situation at hand, and obviates the lengthy analytic multiplicative number theory arguments that used to go into the computation of actual densities. It yields a conceptual interpretation of the formulas obtained, and enables us to extend their range...
Conditions suffisantes d’équirépartition modulo 1 de suites et
Congruence properties of the hyperkloosterman sum
Corrigendum to "An improvement on Olson's constant for ℤₚ ⊕ ℤₚ" (Acta Arith. 141 (2010), 311-319)
Critère de reconnaissabilité de fonctions analytiques et fonctions entières arithmétiques
Cyclotomy of order 15 over , (mod 15).
Dedekind cotangent sums
Dedekind Sums and Class Numbers.
Distributions on Toroidal Groups.
Eigenvalues in the large sieve inequality, II
We explore numerically the eigenvalues of the hermitian formwhen . We improve on the existing upper bound, and produce a (conjectural) plot of the asymptotic distribution of its eigenvalues by exploiting fairly extensive computations. The main outcome is that this asymptotic density most probably exists but is not continuous with respect to the Lebesgue measure.
Estimation of some exponential sums containing the fractional part function and some other "non-standard" exponential sums
Evaluation of two trigonometric sums
Exact exponent in the remainder term of Gelfond's digit theorem in the binary case
Explicit evaluation of certain exponential sums.
Exponential sums associated with the Dedekind zeta-functions.