# Density of positive diagonal binary quadratic forms.

## 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:** Robert Vaughan, Penn State

**Abstract:** We are concerned with which $n$ which can be represented in the form $x^2+zy^2=n$ where $z$ is generally small compared with the size of $n$. We show that almost all $n$ have such a representation with $z<(\log n) (\log\log n)^{3+\delta}$ and that a positive proportion do with $z\ll (\log n)(\log\log n)$. This is joint work with Brandon Hanson.

## Room Reservation Information

**Room Number:** 116 Osmond

**Date:** 08/31/2017

**Time:** 11:00am - 11:50am