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The Density of Numbers Represented by Diagonal Forms of Large Degree
- Source :
- Mathematika 64 (2018) 542-550
- Publication Year :
- 2017
-
Abstract
- 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 $k$.<br />Comment: 7 pages
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- Mathematika 64 (2018) 542-550
- Publication Type :
- Report
- Accession number :
- edsarx.1706.04173
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1112/S0025579318000190