Frits Beukers, Marc Houben, Armin Straub — Acta Arithmetica — Volume 184, 2018, Pages 341-362
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 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.Download
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BibTeX
@article{gausscongruences-2018,
author = {Frits Beukers and Marc Houben and Armin Straub},
title = {Gauss congruences for rational functions in several variables},
journal = {Acta Arithmetica},
year = {2018},
volume = {184},
pages = {341--362},
doi = {10.4064/aa170614-13-7},
}