Waring–Goldbach Problem with Piatetski-Shapiro Primes
Yıldırım Akbal1 ; Ahmet M. Güloğlu1
1 Department of Mathematics Bilkent University 06800 Bilkent, Ankara, Turkey
Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 2, pp. 449-467.

Dans cet article nous donnons une formule asymptotique pour le nombre de représentations d’un grand entier comme somme de puissances identiques des nombres premiers de Piatetski-Shapiro, établissant donc une variante du problème de Waring–Goldbach pour des suites clairsemées de nombres premiers.

In this paper, we exhibit an asymptotic formula for the number of representations of a large integer as a sum of a fixed power of Piatetski-Shapiro primes, thereby establishing a variant of Waring–Goldbach problem with primes from a sparse sequence.

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DOI : 10.5802/jtnb.1033
Classification : 11P32, 11P05, 11P55, 11L03, 11L07, 11L15, 11L20, 11B83
Mots clés : Waring–Goldbach Problem, Piatetski-Shapiro Primes, Circle Method, Weyl Sums, Exponential Sums, van der Corput’s Method, Vinogradov’s Mean value theorem
Yıldırım Akbal 1 ; Ahmet M. Güloğlu 1

1 Department of Mathematics Bilkent University 06800 Bilkent, Ankara, Turkey
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     journal = {Journal de th\'eorie des nombres de Bordeaux},
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Yıldırım Akbal; Ahmet M. Güloğlu. Waring–Goldbach Problem with Piatetski-Shapiro Primes. Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 2, pp. 449-467. doi : 10.5802/jtnb.1033. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1033/

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