Séminaire Lotharingien de Combinatoire, 78B.54 (2017), 12 pp.
Boris Adamczewski, Jason P. Bell,
Éric Delaygue and Frédéric Jouhet
Congruences Modulo Cyclotomic Polynomials and Algebraic Independence for q-Series
We prove congruence relations modulo cyclotomic polynomials for
multisums of q-factorial ratios, therefore generalizing many
well-known p-Lucas congruences. Such congruences connect various
classical generating series to their q-analogs. Using this, we
prove a propagation phenomenon: when these generating series are
algebraically independent, this is also the case for their
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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