$\ell^p(\mathbb{Z}^n)$-estimate for long $r$-variational seminorm of discrete Birch-Magyar averages
Abstract
We prove $\ell^p(\mathbb{Z}^n)-$estimates for long $r$-variational seminorm of two families of averages: discrete Birch-Magyar averages, for $r>max\{p,p'\}$ with $p>\frac{2c_{\mathfrak{R}}-2}{2c_{\mathfrak{R}}-3}$ and discrete Hardy-Littlewood type averages over certain algebraic varieties, for $r>max\{p,p'\}$ with $p>1$. Further, we discuss an application of these results in ergodic theory.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Nonlinear Partial Differential Equations
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 2 January 2026
- Document type
- Preprint