Gauss congruences for rational functions in several variables
Volume 184 / 2018
Abstract
We investigate necessary as well as sufficient conditions under which the Laurent series coefficients 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.