THE DENSITY of NUMBERS REPRESENTED by DIAGONAL FORMS of LARGE DEGREE

Brandon Hanson; Asif Zaman

doi:10.1112/S0025579318000190

THE DENSITY of NUMBERS REPRESENTED by DIAGONAL FORMS of LARGE DEGREE

Brandon Hanson, Asif Zaman

Mathematics

Research output: Contribution to journal › Article

Abstract

Let s ≥ 3 be a fixed positive integer and let a ₁ ; ⋯ ; a _s ϵ Z be arbitrary. We show that, on average over k, the density of numbers represented by the degree k diagonal form a ₁ x ^k ₁ + · · · + a _s x ^k _s decays rapidly with respect to k.

Original language	English (US)
Pages (from-to)	542-550
Number of pages	9
Journal	Mathematika
Volume	64
Issue number	2
DOIs	https://doi.org/10.1112/S0025579318000190
Publication status	Published - Jan 1 2018

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All Science Journal Classification (ASJC) codes

Mathematics(all)

Cite this

Hanson, B., & Zaman, A. (2018). THE DENSITY of NUMBERS REPRESENTED by DIAGONAL FORMS of LARGE DEGREE. Mathematika, 64(2), 542-550. https://doi.org/10.1112/S0025579318000190

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Access to Document

10.1112/S0025579318000190