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 › peer-review

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
State	Published - 2018

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1112/S0025579318000190

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title = "THE DENSITY of NUMBERS REPRESENTED by DIAGONAL FORMS of LARGE DEGREE",

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.",

author = "Brandon Hanson and Asif Zaman",

note = "Publisher Copyright: {\textcopyright} University College London 2018.",

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language = "English (US)",

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AU - Hanson, Brandon

AU - Zaman, Asif

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PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

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U2 - 10.1112/S0025579318000190

DO - 10.1112/S0025579318000190

M3 - Article

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SP - 542

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JO - Mathematika

JF - Mathematika

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ER -

THE DENSITY of NUMBERS REPRESENTED by DIAGONAL FORMS of LARGE DEGREE

Abstract

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