**Gauss congruences for rational functions in several variables**

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

Link | Size | Description | Hits |
---|---|---|---|

gausscongruences.pdf | 381.93 KB | Preprint (PDF, 20 pages) | 1041 |

## 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}, }