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

Abstract. 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 q-analogs.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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