Gauss congruences for rational functions in several variables
Tom 184 / 2018
Streszczenie
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.