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Number Theory Seminar

Thursday, June 14, 2018
4:00pm to 5:00pm
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Building 15, Room 104
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.

For more information, please contact Mathematics Dept. by phone at 626-395-4335 or by email at [email protected].