Congruences modulo cyclotomic polynomials and algebraic independence for $q$-series
Combinatorics
2017-01-24 v1 Number Theory
Abstract
We prove congruence relations modulo cyclotomic polynomials for multisums of -factorial ratios, therefore generalizing many well-known -Lucas congruences. Such congruences connect various classical generating series to their -analogs. Using this, we prove a propagation phenomenon: when these generating series are algebraically independent, this is also the case for their -analogs.
Cite
@article{arxiv.1701.06378,
title = {Congruences modulo cyclotomic polynomials and algebraic independence for $q$-series},
author = {Boris Adamczewski and Jason P. Bell and Éric Delaygue and Frédéric Jouhet},
journal= {arXiv preprint arXiv:1701.06378},
year = {2017}
}
Comments
Extended abstract submitted to FPSAC 2017