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Acta Arithmetica
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Acta Arithmetica
Article . 2003 . Peer-reviewed
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https://dx.doi.org/10.4064/aa1...
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On the Waring–Goldbach problem with small non-integer exponent

On the Waring-Goldbach problem with small non-integer exponent
descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2003 English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Acta Arithmetica, volume 108, pages 297-302 (issn: 0065-1036, eissn: 1730-6264, Copyright policy )
Authors: Garaev, M. Z.;

doi: 10.4064/aa108-3-8

On the Waring–Goldbach problem with small non-integer exponent

Abstract

Let \(c>1\) be non-integer and denote by \(H(c)\) the least \(k\) such that the inequality \[ |p_1^c + p_2^c + \cdots + p_k^c - N|0\) and \(N> N_0(c, \varepsilon)\). In 1952 \textit{I. I. Piatetski-Shapiro} [Mat. Sb., N. Ser. 30, 105-120 (1952; Zbl 0047.28001)] proved that if ~\(1

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Keywords

Waring's problem and variants, Goldbach-type theorems; other additive questions involving primes

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    popularity
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    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
18
Top 10%
Top 10%
Average
bronze