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.

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 $g\ge 2$.

DOI: 10.5802/jtnb.800
Maurizio Laporta 1

1 Dipartimento di Matematica e Appl.“R. Caccioppoli” Università degli Studi di Napoli “Federico II” Via Cinthia, 80126 Napoli, Italy
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Maurizio Laporta. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.800/

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