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 - Jan 1 2018

All Science Journal Classification (ASJC) codes

Mathematics(all)

Access to Document

10.1112/S0025579318000190

Fingerprint Dive into the research topics of 'THE DENSITY of NUMBERS REPRESENTED by DIAGONAL FORMS of LARGE DEGREE'. Together they form a unique fingerprint.

Cite this

@article{ccf6b09db68140a79696bd220def0416,

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",

year = "2018",

month = jan,

day = "1",

doi = "10.1112/S0025579318000190",

language = "English (US)",

volume = "64",

pages = "542--550",

journal = "Mathematika",

issn = "0025-5793",

publisher = "University College London",

number = "2",

}

TY - JOUR

T1 - THE DENSITY of NUMBERS REPRESENTED by DIAGONAL FORMS of LARGE DEGREE

AU - Hanson, Brandon

AU - Zaman, Asif

PY - 2018/1/1

Y1 - 2018/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=85064160488&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064160488&partnerID=8YFLogxK

U2 - 10.1112/S0025579318000190

DO - 10.1112/S0025579318000190

M3 - Article

AN - SCOPUS:85064160488

VL - 64

SP - 542

EP - 550

JO - Mathematika

JF - Mathematika

SN - 0025-5793

IS - 2

ER -