S. Akhtari

collaborators

Showing math.NTShow all

4 papers · 1 filter

math.NT2011

Upper bounds for the number of solutions to quartic Thue equations

Shabnam Akhtari

We will give upper bounds for the number of integral solutions to quartic Thue equations. Our main tool here is a logarithmic curve $ϕ (x, y)$ that allows us to use the theory of li…

math.NT2010

Representation of Unity by Binary Forms

Shabnam Akhtari

In this paper, it is shown that if F(x , y) is an irreducible binary form with integral coefficients and degree $n \geq 3$ , then provided that the absolute value of the discriminan…

math.NT2009

Cubic Thue Equations

Shabnam Akhtari

We revisit a work by R. Okazaki and prove that for every cubic binary form F(x, y) with large enough discriminant, the Thue equation |F(x, y)| = 1 has at most 7 solutions in intege…

math.NT2009

The Diophantine equation $a X^{4} - b Y^{2} = 1$

Shabnam Akhtari

As an application of the method of Thue-Siegel, we will resolve a conjecture of Walsh to the effect that the Diophantine equation $a X^{4} - b Y^{2} = 1$ , for fixed positive integers $a$ …

Upper bounds for the number of solutions to quartic Thue equations

Representation of Unity by Binary Forms

Cubic Thue Equations

The Diophantine equation aX4−bY2=1

The Diophantine equation $a X^{4} - b Y^{2} = 1$