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.
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.
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Classification: 11P32, 11P05, 11P55, 11L03, 11L07, 11L15, 11L20, 11B83
Keywords: Waring–Goldbach Problem, Piatetski-Shapiro Primes, Circle Method, Weyl Sums, Exponential Sums, van der Corput’s Method, Vinogradov’s Mean value theorem
Author's affiliations:
@article{JTNB_2018__30_2_449_0, author = {Y{\i}ld{\i}r{\i}m Akbal and Ahmet M. G\"ulo\u{g}lu}, 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}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1033/} }
TY - JOUR TI - Waring–Goldbach Problem with Piatetski-Shapiro Primes JO - Journal de Théorie des Nombres de Bordeaux PY - 2018 DA - 2018/// SP - 449 EP - 467 VL - 30 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1033/ UR - https://doi.org/10.5802/jtnb.1033 DO - 10.5802/jtnb.1033 LA - en ID - JTNB_2018__30_2_449_0 ER -
Yıldırım Akbal; Ahmet M. Güloğlu. Waring–Goldbach Problem with Piatetski-Shapiro Primes. Journal de Théorie des Nombres de Bordeaux, Volume 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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