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Gauss Congruences for Rational Functions in Several Variables by Beukers, Frits; Houben, Marc; Straub, Armin is a scholarly article available to read on EtoBox.

What is Gauss Congruences for Rational Functions in Several Variables about?

We investigate necessary as well as sufficient conditions under which the Laurent series coefficients $f_{\boldsymbol{n}}$ associated to a multivariate rational function satisfy Gauss congruences, that is $f_{\boldsymbol{m}p^r} \equiv f_{\boldsymbol{m}p^{r-1}}$ modulo $p^r$. 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 in the case that $Q$ is linear in each variable.

Author

Beukers, Frits; Houben, Marc; Straub, Armin

Published

2017

Language

EN