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arXiv · 2601.00654

$\ell^p(\mathbb{Z}^n)$-estimate for long $r$-variational seminorm of discrete Birch-Magyar averages

Ankit Bhojak·Siddhartha Samanta·Saurabh Shrivastava
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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.

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Ankit Bhojak, Siddhartha Samanta, Saurabh Shrivastava. 2026-01-02. $\ell^p(\mathbb{Z}^n)$-estimate for long $r$-variational seminorm of discrete Birch-Magyar averages. https://arxiv.org/abs/2601.00654

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