Javier Cilleruelo

Trigonometric polynomials and lattice points

In this paper we study the distribution of lattice points on arcs of circles centered at the origin. We show that on such a circle of radius R, an arc whose length is smaller than V2Rl12-l(4[m/2]+2) contains, at most, m lattice points. We use the same method to obtain sharp L4-estimates for uncompleted, Gaussian sums

On Monochromatic solutions of equations in groups

We show that the number of monochromatic solutions of the equation x α1 1 x α2 2 ··· x αr r = g in a 2-coloring of a finite group G ,w here α1 ,...,α r are permutations and g ∈ G, depends only on the cardinalities of the chromatic classes but not on their distribution. We give some applications to arithmetic Ramsey statements.

Perfect difference sets constructed from Sidon sets

AbstractA set

Lattice points on circles

\mathcal{A}

DENSE INFINITE Bh SEQUENCES

of positive integers is a perfect difference set if every nonzero integer has a unique representation as the difference of two elements of

Bh [g] sequences

\mathcal{A}