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Representation of integers by binary forms

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Speaker: 
Shabnam Akhtari
Affiliation: 
University of Oregon/MPIM
Date: 
Wed, 2018-11-14 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

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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