Gauss congruences for rational functions in several variables
Volume 184 / 2018
Acta Arithmetica 184 (2018), 341-362
MSC: 11A07, 11B37.
DOI: 10.4064/aa170614-13-7
Published online: 20 August 2018
Abstract
We investigate necessary as well as sufficient conditions under which the Laurent series coefficients $f_{\boldsymbol{n}}$ associated to a multivariate rational function satisfy the Gauss congruences, that is, $f_{\boldsymbol{m}p^r} \equiv f_{\boldsymbol{m}p^{r - 1}} ({\rm mod}\ {p^r})$. For instance, we show that these congruences hold for certain determinants of logarithmic derivatives. As an application, we completely classify rational functions $P / Q$ satisfying the Gauss congruences when $Q$ is linear in each variable.
