arminstraub.com

Gauss congruences for rational functions in several variables

Gauss congruences for rational functions in several variables
Frits Beukers, Marc Houben, Armin Straub — Acta Arithmetica — 2018

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

LinkSizeDescriptionHits
381.93 KB Preprint (PDF, 20 pages) 298

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},
    doi = {10.4064/aa170614-13-7},
}