Thursday, June 14, 2018
4:00 PM -
5:00 PM
Building 15, Room 104
Number Theory Seminar
Series: Number Theory Seminar Series
Representation of integers by binary forms
Let F(x, y) be an irreducible binary form with integer coefficients and of degree at least 3. By a well-known result of Thue, the equation F(x, y) = m has only finitely many solutions in integers x and y. I will discuss some old and new quantitative results on the number of solutions of such equations. I will also talk about my joint work with Manjul Bhargava, where we use these bounds to show that many equations of the shape F(x, y) = m have no solutions.
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For more information, please contact Mathematics Dept. by phone at 626-395-4335 or by email at [email protected].