Thursday, June 14, 2018
4:00 pm
Building 15, Room 104 – Building 15

Number Theory Seminar

Representation of integers by binary forms
Shabnam Akhtari, Department of Mathematics, University of Oregon

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.

Contact Mathematics Dept. mathinfo@caltech.edu at 626-395-4335
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