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

Ankit Bhojak, Siddhartha Samanta, Saurabh Shrivastava

We prove ${\ell }^p({\mathbb{Z}}^n)-$estimates for long $r$-variational seminorm of two families of averages: discrete Birch-Magyar averages, for $r>max\{p,p^{\prime }\}$ with $p>\frac{2c_{\math…