7 papers
A lattice point counting approach for the study of the number of self-avoiding walks on
Youssef Lazar
We reduce the problem of counting self-avoiding walks in the square lattice to a problem of counting the number of integral points in multidimensional domains. We obtain an asympto…
Simultaneous diophantine approximation for a restricted class of pairs of real numbers
Youssef Lazar
We prove that the Littlewood conjecture is satisfied for a restricted class of pairs of badly approximable numbers. We use the localization of the roots of a cubic equation…
Explicit solutions to the Oppenheim conjecture for indefinite ternary diagonal forms
Youssef Lazar
We prove the Oppenheim conjecture for indefinite ternary diagonal forms of the type where is an irrational number. Our method is explicit in the sense th…
Geometric considerations around the Littlewood conjecture
Youssef Lazar
In this paper we adopt a geometric point of view regarding a famous conjecture due to Littlewood in diophantine approximation of real numbers. Following the spirit of the geometric…
A remark on a conjecture of Erdős and Straus
Youssef Lazar
The aim of this note is to show that given a positive integer , the positive integral solutions of the diophantine equation cannot have solution suc…
On the density of S-adic integers near some projective G-varieties
Youssef Lazar
We provide some general conditions which ensure that a system of inequalities involving homogeneous polynomials with coefficients in a S-adic field has nontrivial S-integral soluti…
Values of pairs involving one quadratic and one linear form at S-integral points
Youssef Lazar
We prove the existence of S-integral solutions of simultaneous diophantine inequalities for pairs (Q,L) involving one quadratic form and one linear form satisfying some arithmetico…