A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Roth-type theorem for nonlinear equations in Piatetski-Shapiro primes
Tekijät: Ren, Xiumin; Sun, Yu-Chen; Zhang, Qingqing; Zhang, Rui
Kustantaja: WORLD SCIENTIFIC PUBL CO PTE LTD
Kustannuspaikka: SINGAPORE
Julkaisuvuosi: 2024
Journal: International Journal of Number Theory
Tietokannassa oleva lehden nimi: INTERNATIONAL JOURNAL OF NUMBER THEORY
Lehden akronyymi: INT J NUMBER THEORY
Sivujen määrä: 16
ISSN: 1793-0421
eISSN: 1793-7310
DOI: https://doi.org/10.1142/S1793042125500447
Verkko-osoite: https://doi.org/10.1142/S1793042125500447
We consider the nonlinear diophantine equation c(1)p(1)(d) + c(2)p(2)(d) + center dot center dot center dot + c(s)p(s)(d) = 0 with c(1),c(2),...,c(s) is an element of Z being non-zero and satisfying c(1) + c(2) + center dot center dot center dot + c(s) = 0. We show that for s >= 2(sic)d(2)/2(sic) + 1 and c is an element of (1, 1 + c(0)(d,s)), if the equation has only K-trivial solutions in a subset epsilon of Piatetski-Shapiro primes up to x corresponding to c, then |A|<< x(c)(1)/log x (log log log log x)(2-s/dc +epsilon).
Julkaisussa olevat rahoitustiedot:
This work is supported by the National Natural Science Foundation of China (Grant Nos. 11871307 and 12031008) and the National Key Research and Development Program of China (Grant No. 2021YFA1000700). The second author was supported by UTUGS funding, working in the Academy of Finland Project No. 333707
