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Acta Mathematica Hungarica

, Volume 159, Issue 1, pp 150–163 | Cite as

Sums of four prime cubes in short intervals

  • A. LanguascoEmail author
  • A. Zaccagnini
Article

Abstract

We prove that a suitable asymptotic formula for the average number of representations of integers \(n=p_{1}^{3}+p_{2}^{3}+p_{3}^{3}+p_{4}^{3}\), where \(p_1\), \(p_2\), \(p_3\), \(p_4\) are prime numbers, holds in intervals shorter than the the ones previously known.

Key words and phrases

Waring–Goldbach problem Hardy–Littlewood method 

Mathematics Subject Classification

primary 11P32 secondary 11P55 11P05 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica “Tullio Levi-Civita”Universitá di PadovaPadovaItaly
  2. 2.Dipartimento di Scienze Matematiche, Fisiche e InformaticheUniversitá di ParmaParmaItaly

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