Short intervals asymptotic formulae for binary problems with prime powers
Alessandro Languasco1 ; Alessandro Zaccagnini2
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.

We prove results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms n=p1ℓ1+p2ℓ2 and n=pℓ1+mℓ2, where ℓ1,ℓ2 are fixed integers, p,p1,p2 are prime numbers and m is an integer.

Nous montrons des formules asymptotiques dans des intervalles courts pour le nombre moyen de représentations des entiers de la forme n=p1ℓ1+p2ℓ2 et n=pℓ1+mℓ2, où ℓ1,ℓ2 sont des entiers fixés, p,p1,p2 sont des nombres premiers et m est un entier.

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DOI : 10.5802/jtnb.1041
Classification : 11P32, 11P55, 11P05
Mots-clés : Waring-Goldbach problem, Hardy–Littlewood method

Alessandro Languasco 1 ; Alessandro Zaccagnini 2

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
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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, Tome 30 (2018) no. 2, pp. 609-635. doi : 10.5802/jtnb.1041. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1041/

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