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
Mots-clés : Waring–Goldbach Problem, Piatetski-Shapiro Primes, Circle Method, Weyl Sums, Exponential Sums, van der Corput’s Method, Vinogradov’s Mean value theorem
@article{JTNB_2018__30_2_449_0, author = {Akbal, Y{\i}ld{\i}r{\i}m and G\"ulo\u{g}lu, Ahmet M.}, title = {Waring{\textendash}Goldbach {Problem} with {Piatetski-Shapiro} {Primes}}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {449--467}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {30}, number = {2}, year = {2018}, doi = {10.5802/jtnb.1033}, mrnumber = {3891321}, zbl = {1443.11207}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jtnb.1033/} }
TY - JOUR AU - Akbal, Yıldırım AU - Güloğlu, Ahmet M. TI - Waring–Goldbach Problem with Piatetski-Shapiro Primes JO - Journal de théorie des nombres de Bordeaux PY - 2018 SP - 449 EP - 467 VL - 30 IS - 2 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.1033/ DO - 10.5802/jtnb.1033 LA - en ID - JTNB_2018__30_2_449_0 ER -
%0 Journal Article %A Akbal, Yıldırım %A Güloğlu, Ahmet M. %T Waring–Goldbach Problem with Piatetski-Shapiro Primes %J Journal de théorie des nombres de Bordeaux %D 2018 %P 449-467 %V 30 %N 2 %I Société Arithmétique de Bordeaux %U http://www.numdam.org/articles/10.5802/jtnb.1033/ %R 10.5802/jtnb.1033 %G en %F JTNB_2018__30_2_449_0
Akbal, Yıldırım; Güloğlu, Ahmet M. 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. http://www.numdam.org/articles/10.5802/jtnb.1033/
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