The Density of Numbers Represented by Diagonal Forms of Large Degree

Abstract

Let $s\ge 3$ be a fixed positive integer and $a_1,\dots ,a_s\in \mathbb{Z}$ be arbitrary. We show that, on average over $k$, the density of numbers represented by the degree $k$ diagonal form \[ a_1 x_1^k + \cdots + a_s x_s^k \] decays rapidly with respect to $k$.

7 pages

References in corpus (1)

• An explicit bound for the least prime ideal in the Chebotarev density theorem