Representation of integers by binary forms

Speaker: Dr. Shabnam Akhtari (MPIM)

Time: 4:00PM
Date: Wed 5th May 2010

Location: Mathematical Sciences Seminar Room

Let F(x,y) be an irreducible binary form with integral coefficients and degree n greater than or equal to 3, then by a well-known result of Thue, the equation F(x,y) = m (m an integer) has finitely many solutions in integers x and y. I shall discuss some methods from Diophantine analysis and geometry of numbers to obtain upper bounds upon the number of integral solutions to such equations. I will pay special attention to quartic forms and describe a general method for finding integral points on elliptic curves by reducing them to quartic Thue equations. Then I will show some results on representation of integers by binary forms.

(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)