Gauss congruences for rational functions in several variables
Abstract
We investigate necessary as well as sufficient conditions under which the Laurent series coefficients fn associated to a multivariate rational function satisfy Gauss congruences, that is fmpr fmpr-1 modulo pr. 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 in the case that Q is linear in each variable.
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