Representation of Unity by Binary Forms

Details Representation of Unity by Binary Forms Representation of Unity by Binary Forms

2010-11-19

arxiv.org/abs/1011.4507v1

Mathematics

Number Theory

Scientific paper

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 discriminant of F is large enough, the equation |F(x , y)| = 1 has at most 11n-2 solutions in integers x and y. We will also establish some sharper bounds when more restrictions are assumed. These upper bounds are derived by combining methods from classical analysis and geometry of numbers. The theory of linear forms in logarithms plays an essential role in studying the geometry of our Diophantine equations.

Affiliated with

Also associated with

No associations

Rating

Representation of Unity by Binary Forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Representation of Unity by Binary Forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representation of Unity by Binary Forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-21329