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Alessandro Languasco; Alessandro Zaccagnini
Short intervals asymptotic formulae for binary problems with prime powers
Journal de théorie des nombres de Bordeaux, 30 no. 2 (2018), p. 609-635, doi: 10.5802/jtnb.1041
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Class. Math.: 11P32, 11P55, 11P05
Mots clés: Waring-Goldbach problem, Hardy–Littlewood method

Résumé - Abstract

Nous montrons des formules asymptotiques dans des intervalles courts pour le nombre moyen de représentations des entiers de la forme $n=p_{1}^{\ell _1}+p_{2}^{\ell _2}$ et $n=p^{\ell _1} + m^{\ell _2}$, où $\ell _1, \ell _2$ sont des entiers fixés, $p,p_1,p_2$ sont des nombres premiers et $m$ est un entier.

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