On Some Problems of Gyarmati and Sárközy

Density and ramsey type results on algebraic equations with restricted solution sets

In earlier papers Sárközy studied the solvability of the equations a + b = cd, a ∈ A, b ∈ B, c ∈ C, d ∈ D, resp. ab + 1 = cd, a ∈ A, b ∈ B, c ∈ C, d ∈ D where A,B, C,D are “large” subsets of Fp. Later Gyarmati and Sárközy generalized and extended these problems by studying these equations and also other algebraic equations with restricted solution sets over finite fields. Here we will continue ...

Constructions of Pseudorandom Binary Lattices

Three constructions for binary lattices with strong pseudorandom properties are given. These constructions are the two dimensional extensions and modifications of three of the most important one dimensional constructions. The upper estimates for the pseudorandom measures of the binary lattices constructed are based on the principle that character sums in two variables can be estimated by fixing...

On the correlation of binary sequences, II

This paper concerns the study of the correlation measures of finite binary sequences, more particularily the dependence of correlation measures of even order and correlation measures of odd order. These results generalize previous results due to Gyarmati [7] and to Anantharam [3] and provide a partial answer to a conjecture due to Mauduit [12]. The last part of the paper concerns the generaliza...

Pseudorandomness of binary sequences and their generalization

On sums which are powers