The Density of Numbers Represented by Diagonal Forms of Large Degree. (arXiv:1706.04173v1 [math.NT])

Let $s \geq 3$ 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 $k$.查看全文

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