MATH Seminar

Title: On computations of Shanks and Schmid
Seminar: Algebra and Number Theory
Speaker: Robert Osburn of University College Dublin
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2012-10-30 at 4:00PM
Venue: W306
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Abstract: In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to $x$ which are represented by the quadratic form $X^2+nY^2$, n greater than or equal to 1. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for $n=2$. In this talk, we discuss a proof of the fact that this constant is actually unbounded as one runs through fundamental discriminants with a fixed number of distinct prime divisors. This is joint work with David Brink and Pieter Moree (MPIM).