4 papers
math.NT2021
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…
math.NT2020
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…
math.NT2020
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…
math.NT2019
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…