Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations: three additive equations

Joerg Bruedern; Trevor D Wooley

doi:10.4171/JEMS/813

Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations: three additive equations

Joerg Bruedern, Trevor D Wooley

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Abstract

We establish the non-singular Hasse principle for systems of three diagonal quartic equations in 32 or more variables, subject to a certain rank condition. Our methods employ the arithmetic harmonic analysis of smooth quartic Weyl sums and also a new estimate for their tenth moment.

Original language	English
Pages (from-to)	2333-2356
Number of pages	24
Journal	Journal of the European Mathematical Society
Volume	20
Issue number	10
Early online date	9 Jul 2018
DOIs	https://doi.org/10.4171/JEMS/813
Publication status	Published - 1 Oct 2018

Keywords

Quartic Diophantine equations
Hardy–Littlewood method

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10.4171/JEMS/813

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via EMS at https://www.ems-ph.org/journals/show_issue.php?issn=1435-9855&vol=20&iss=10. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 403 KB

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title = "Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations: three additive equations",

abstract = "We establish the non-singular Hasse principle for systems of three diagonal quartic equations in 32 or more variables, subject to a certain rank condition. Our methods employ the arithmetic harmonic analysis of smooth quartic Weyl sums and also a new estimate for their tenth moment.",

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T1 - Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations

T2 - three additive equations

AU - Bruedern, Joerg

AU - Wooley, Trevor D

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We establish the non-singular Hasse principle for systems of three diagonal quartic equations in 32 or more variables, subject to a certain rank condition. Our methods employ the arithmetic harmonic analysis of smooth quartic Weyl sums and also a new estimate for their tenth moment.

AB - We establish the non-singular Hasse principle for systems of three diagonal quartic equations in 32 or more variables, subject to a certain rank condition. Our methods employ the arithmetic harmonic analysis of smooth quartic Weyl sums and also a new estimate for their tenth moment.

KW - Quartic Diophantine equations

KW - Hardy–Littlewood method

UR - http://arxiv.org/abs/1507.07465

U2 - 10.4171/JEMS/813

DO - 10.4171/JEMS/813

M3 - Article (Academic Journal)

SN - 1435-9855

VL - 20

SP - 2333

EP - 2356

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 10

ER -

Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations: three additive equations

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