Roth-type theorem for nonlinear equations in Piatetski-Shapiro primes
We consider the nonlinear diophantine equation [Formula: see text] with [Formula: see text] being non-zero and satisfying [Formula: see text]. We show that for [Formula: see text] and [Formula: see text], if the equation has only K-trivial solutions in a subset [Formula: see text] of Piatetski-Shapiro primes up to x corresponding to c, then [Formula: see text] [Formula: see text].
Authors
- Rui Zhang (ORCID: https://orcid.org/0000-0003-0684-6579)
- Yu‐Chen Sun (ORCID: https://orcid.org/0000-0001-5994-8961)
- Qingqing Zhang (ORCID: https://orcid.org/0000-0003-3109-4268)
- Xiumin Ren
Institutions
- Shandong University (CN)
- University of Turku (FI)
- Qufu Normal University (CN)
Publication Details
- Journal
- International Journal of Number Theory
- Published
- 2024-11-15
- DOI
- https://doi.org/10.1142/s1793042125500447
- Primary Topic
- advanced mathematical theories
- Type
- article
- Field-Weighted Citation Impact
- 0.00