ON WARING'S PROBLEM: TWO SQUARES AND THREE BIQUADRATES

John B. Friedlander; Trevor D. Wooley

doi:10.1112/S0025579313000089

ON WARING'S PROBLEM: TWO SQUARES AND THREE BIQUADRATES

John B. Friedlander^*
, Trevor D. Wooley

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott-Halberstam conjecture, we show that all large natural numbers n with 8 inverted iota n, n (sic) 2 (mod 3) and n (sic) 14 (mod 16) are the sum of two squares and three biquadrates.

Original language	English
Pages (from-to)	153-165
Number of pages	13
Journal	Mathematika
Volume	60
Issue number	1
DOIs	https://doi.org/10.1112/S0025579313000089
Publication status	Published - Jan 2014

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SUMS
POWERS

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title = "ON WARING'S PROBLEM: TWO SQUARES AND THREE BIQUADRATES",

abstract = "We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott-Halberstam conjecture, we show that all large natural numbers n with 8 inverted iota n, n (sic) 2 (mod 3) and n (sic) 14 (mod 16) are the sum of two squares and three biquadrates.",

keywords = "SUMS, POWERS",

author = "Friedlander, \{John B.\} and Wooley, \{Trevor D.\}",

year = "2014",

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T1 - ON WARING'S PROBLEM: TWO SQUARES AND THREE BIQUADRATES

AU - Friedlander, John B.

AU - Wooley, Trevor D.

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N2 - We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott-Halberstam conjecture, we show that all large natural numbers n with 8 inverted iota n, n (sic) 2 (mod 3) and n (sic) 14 (mod 16) are the sum of two squares and three biquadrates.

AB - We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott-Halberstam conjecture, we show that all large natural numbers n with 8 inverted iota n, n (sic) 2 (mod 3) and n (sic) 14 (mod 16) are the sum of two squares and three biquadrates.

KW - SUMS

KW - POWERS

U2 - 10.1112/S0025579313000089

DO - 10.1112/S0025579313000089

M3 - Article (Academic Journal)

SN - 0025-5793

VL - 60

SP - 153

EP - 165

JO - Mathematika

JF - Mathematika

IS - 1

ER -

ON WARING'S PROBLEM: TWO SQUARES AND THREE BIQUADRATES

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