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.

Nous montrons des formules asymptotiques dans des intervalles courts pour le nombre moyen de représentations des entiers de la forme n=p 1 1 +p 2 2 et n=p 1 +m 2 , où 1 , 2 sont des entiers fixés, p,p 1 ,p 2 sont des nombres premiers et m est un entier.

We prove results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms n=p 1 1 +p 2 2 and n=p 1 +m 2 , where 1 , 2 are fixed integers, p,p 1 ,p 2 are prime numbers and m is an integer.

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DOI : https://doi.org/10.5802/jtnb.1041
Classification : 11P32,  11P55,  11P05
Mots clés : Waring-Goldbach problem, Hardy–Littlewood method
@article{JTNB_2018__30_2_609_0,
     author = {Alessandro Languasco and Alessandro Zaccagnini},
     title = {Short intervals asymptotic formulae for binary problems with prime powers},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {609--635},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {30},
     number = {2},
     year = {2018},
     doi = {10.5802/jtnb.1041},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1041/}
}
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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