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, Volume 24 (2012) no. 2, p. 355-368

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 ${p}_{1}\equiv l\phantom{\rule{0.277778em}{0ex}}\left(\mathrm{mod}\phantom{\rule{0.277778em}{0ex}}k\right)$, under suitable hypothesis on $s=s\left(g\right)$ for every integer $g\ge 2$.

Nous démontrons un théorème de type Bombieri- Vinogradov sur le nombre de représentations d’un entier $N$ sous la forme $N={p}_{1}^{g}+{p}_{2}^{g}+\cdots +{p}_{s}^{g}$ avec ${p}_{1},{p}_{2},\cdots ,{p}_{s}$ des nombres premiers et ${p}_{1}\equiv l\phantom{\rule{0.277778em}{0ex}}\left(\mathrm{mod}\phantom{\rule{0.277778em}{0ex}}k\right)$, sous une hypothèse convenable $s=s\left(g\right)$ pour chaque entier $g\ge 2$.

@article{JTNB_2012__24_2_355_0,
author = {Laporta, Maurizio},
title = {On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression},
journal = {Journal de th\'eorie des nombres de Bordeaux},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {24},
number = {2},
year = {2012},
pages = {355-368},
doi = {10.5802/jtnb.800},
mrnumber = {2950696},
zbl = {pre06099148},
language = {en},
url = {http://www.numdam.org/item/JTNB_2012__24_2_355_0}
}

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, Volume 24 (2012) no. 2, pp. 355-368. doi : 10.5802/jtnb.800. http://www.numdam.org/item/JTNB_2012__24_2_355_0/

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