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The least common multiple of a quadratic sequence
Abstract For any irreducible quadratic polynomial f(x) in ℤ[x], we obtain the estimate log l.c.m.(f(1),…,f(n))=nlog n+Bn+o(n), where B is a constant depending on f.
Sidon sets in Nd
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)
Combinatorial problems in finite fields and Sidon sets
We use Sidon sets to present an elementary method to study some combinatorial problems in finite fields, such as sum product estimates, solvability of some equations and the distribution of their
Upper and Lower Bounds for Finite Bh[g] Sequences
Abstract We give a non-trivial upper bound for Fh(g,N), the size of a Bh[g] subset of {1,…,N}, when g>1. In particular, we prove F2(g,N)⩽1.864(gN)1/2+1, and F h (g,N)⩽ 1 (1+cos h (π/h)) 1/h (hh!gN)
Congruences involving product of intervals and sets with small multiplicative doubling modulo a prime and applications
Abstract In this paper we obtain new upper bound estimates for the number of solutions of the congruence $$\begin{equation} x\equiv y r\pmod p;\quad x,y\in \mathbb{N},\quad x,y\le H,\quad r\in
Concentration of Points on Two and Three Dimensional Modular Hyperbolas and Applications
AbstractLet p be a large prime number, K, L, M, λ be integers with 1 ≤ M ≤ p and gcd(λ, p) = 1. The aim of our paper is to obtain sharp upper bound estimates for the number I2(M; K, L) of solutions
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
Lattice points on circles, squares in arithmetic progressions and sumsets of squares
22 paginas, 1 figura.-- 2000 Mathematics Subject Classification:11N36.-- En: Andrew Granwille, Melvyn B. Nathanson y Jozsef Solymosi (Eds.).
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