Short intervals asymptotic formulae for binary problems with prime powers

Languasco, Alessandro¹ ; Zaccagnini, Alessandro²

¹ Università di Padova Dipartimento di Matematica “Tullio Levi-Civita” Via Trieste 63 35121 Padova, Italy
² Università di Parma Dipartimento di Scienze Matematiche Fisiche e Informatiche Parco Area delle Scienze, 53/a 43124 Parma, Italy

Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 2, pp. 609-635.

Abstract (VO)

We prove results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms $n=p_1^{{\ell }_1}+p_2^{{\ell }_2}$ and $n=p^{{\ell }_1}+m^{{\ell }_2}$, where ${\ell }_1,{\ell }_2$ are fixed integers, $p,p_1,p_2$ are prime numbers and $m$ is an integer.

Résumé

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.

Détail

Reçu le : 2016-11-20
Révisé le : 2017-11-16
Accepté le : 2017-11-29
Publié le : 2018-12-07
DOI : 10.5802/jtnb.1041

Classification : 11P32, 11P55, 11P05
Keywords: Waring-Goldbach problem, Hardy–Littlewood method

Licence : CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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