Mock Heegner points and Sylvester's conjecture

Algebra and Number Theory Seminar

Meeting Details

For more information about this meeting, contact Kendra Stauffer, Robert Vaughan, Mihran Papikian, Ae Ja Yee, Kirsten Eisentraeger, Jack Huizenga.

Speaker: John Voight, Dartmouth College

Abstract: We consider the classical Diophantine problem of writing positive integers $n$ as the sum of two rational cubes, i.e.\ $n=x^3+y^3$ for $x,y \in {\mathbb Q}$. A conjecture attributed to Sylvester asserts that a rational prime $p>3$ can be so expressed if $p \equiv 4,7,8 \pmod{9}$. The theory of mock Heegner points gives a method for exhibiting such a pair $(x,y)$ in certain cases. We prove Sylvester's conjecture in the case that $p \equiv 4,7 \pmod{9}$ and $3$ is not a cube modulo $p$. This is joint work with Samit Dasgupta.

Room Reservation Information

Room Number: 116 Osmond

Date: 02/01/2018

Time: 11:00am - 11:50am