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

Laporta, Maurizio

Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 2, pp. 355-368.

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 $p_1\equiv l\left(\mathrm{mod}k\right)$, sous une hypothèse convenable $s=s\left(g\right)$ pour chaque entier $g\ge 2$.

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 $p_1\equiv l\left(\mathrm{mod}k\right)$, under suitable hypothesis on $s=s\left(g\right)$ for every integer $g\ge 2$.

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