On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression

Maurizio Laporta[1]

  • [1] Dipartimento di Matematica e Appl.“R. Caccioppoli” Università degli Studi di Napoli “Federico II” Via Cinthia, 80126 Napoli, Italy

Journal de Théorie des Nombres de Bordeaux (2012)

  • Volume: 24, Issue: 2, page 355-368
  • ISSN: 1246-7405

Abstract

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We prove a Bombieri-Vinogradov type theorem for the number of representations of an integer N in the form N = p 1 g + p 2 g + ... + p s g with p 1 , p 2 , ... , p s prime numbers such that p 1 ≡ l ( mod k ) , under suitable hypothesis on s = s ( g ) for every integer g ≥ 2 .

How to cite

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Laporta, Maurizio. "On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression." Journal de Théorie des Nombres de Bordeaux 24.2 (2012): 355-368. <http://eudml.org/doc/251079>.

@article{Laporta2012,
abstract = {We prove a Bombieri-Vinogradov type theorem for the number of representations of an integer $N$ in the form $N=p_1^\{g\}+p_2^\{g\}+\ldots +p_s^\{g\}$ with $p_1,p_2,\ldots , p_s$ prime numbers such that $p_1\equiv l\; (\{\rm mod\}\; k)$, under suitable hypothesis on $s = s(g)$ for every integer $g\ge 2$.},
affiliation = {Dipartimento di Matematica e Appl.“R. Caccioppoli” Università degli Studi di Napoli “Federico II” Via Cinthia, 80126 Napoli, Italy},
author = {Laporta, Maurizio},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Waring-Goldbach problem; circle method; prime},
language = {eng},
month = {6},
number = {2},
pages = {355-368},
publisher = {Société Arithmétique de Bordeaux},
title = {On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression},
url = {http://eudml.org/doc/251079},
volume = {24},
year = {2012},
}

TY - JOUR
AU - Laporta, Maurizio
TI - On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2012/6//
PB - Société Arithmétique de Bordeaux
VL - 24
IS - 2
SP - 355
EP - 368
AB - We prove a Bombieri-Vinogradov type theorem for the number of representations of an integer $N$ in the form $N=p_1^{g}+p_2^{g}+\ldots +p_s^{g}$ with $p_1,p_2,\ldots , p_s$ prime numbers such that $p_1\equiv l\; ({\rm mod}\; k)$, under suitable hypothesis on $s = s(g)$ for every integer $g\ge 2$.
LA - eng
KW - Waring-Goldbach problem; circle method; prime
UR - http://eudml.org/doc/251079
ER -

References

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