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, Volume 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=p 1 ℓ 1 +p 2 ℓ 2 and n=p ℓ 1 +m ℓ 2 , where ℓ 1 ,ℓ 2 are fixed integers, p,p 1 ,p 2 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=p 1 ℓ 1 +p 2 ℓ 2 et n=p ℓ 1 +m ℓ 2 , où ℓ 1 ,ℓ 2 sont des entiers fixés, p,p 1 ,p 2 sont des nombres premiers et m est un entier.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1041
Classification: 11P32, 11P55, 11P05
Keywords: 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
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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, Volume 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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