Hua's lemma and simultaneous diagonal equations

J Brudern; TD Wooley

doi:10.1112/S002460930100889X

Hua's lemma and simultaneous diagonal equations

J Brudern
, TD Wooley

Research output: Contribution to journal › Article (Academic Journal) › peer-review

7 Citations (Scopus)

Abstract

This paper concerns systems of r homogeneous diagonal equations of degree k in s variables, with integer coefficients. Subject to a suitable non-singularity condition, it is shown that the expected asymptotic formula holds for the number of such systems inside a box [-P, P](s), provided only that s > (3r + 1)2(k-2). By way of comparison, classical methods based on the use of Hua's lemma would establish a similar conclusion, provided instead that s > r2(k).

Translated title of the contribution	Hua's lemma and simultaneous diagonal equations
Original language	English
Pages (from-to)	279 - 283
Number of pages	5
Journal	Bulletin of the London Mathematical Society
Volume	34 (3)
DOIs	https://doi.org/10.1112/S002460930100889X
Publication status	Published - May 2002

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Publisher: London Math Soc

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http://blms.oxfordjournals.org/cgi/reprint/34/3/279

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title = "Hua's lemma and simultaneous diagonal equations",

abstract = "This paper concerns systems of r homogeneous diagonal equations of degree k in s variables, with integer coefficients. Subject to a suitable non-singularity condition, it is shown that the expected asymptotic formula holds for the number of such systems inside a box [-P, P](s), provided only that s > (3r + 1)2(k-2). By way of comparison, classical methods based on the use of Hua's lemma would establish a similar conclusion, provided instead that s > r2(k).",

author = "J Brudern and TD Wooley",

note = "Publisher: London Math Soc",

year = "2002",

month = may,

doi = "10.1112/S002460930100889X",

language = "English",

volume = "34 (3)",

pages = "279 -- 283",

journal = "Bulletin of the London Mathematical Society",

issn = "1469-2120",

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T1 - Hua's lemma and simultaneous diagonal equations

AU - Brudern, J

AU - Wooley, TD

N1 - Publisher: London Math Soc

PY - 2002/5

Y1 - 2002/5

N2 - This paper concerns systems of r homogeneous diagonal equations of degree k in s variables, with integer coefficients. Subject to a suitable non-singularity condition, it is shown that the expected asymptotic formula holds for the number of such systems inside a box [-P, P](s), provided only that s > (3r + 1)2(k-2). By way of comparison, classical methods based on the use of Hua's lemma would establish a similar conclusion, provided instead that s > r2(k).

AB - This paper concerns systems of r homogeneous diagonal equations of degree k in s variables, with integer coefficients. Subject to a suitable non-singularity condition, it is shown that the expected asymptotic formula holds for the number of such systems inside a box [-P, P](s), provided only that s > (3r + 1)2(k-2). By way of comparison, classical methods based on the use of Hua's lemma would establish a similar conclusion, provided instead that s > r2(k).

U2 - 10.1112/S002460930100889X

DO - 10.1112/S002460930100889X

M3 - Article (Academic Journal)

SN - 1469-2120

VL - 34 (3)

SP - 279

EP - 283

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

ER -

Hua's lemma and simultaneous diagonal equations

Abstract

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