Geodesic
Congruences Modulo Cyclotomic Polynomials and Algebraic Independence for q-Series
Séminaire lotharingien de combinatoire, 78B (2017)

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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. 

@article{SLC_2017_78B_a53,
     author = {Boris Adamczewski and Jason P. Bell and \'Eric Delaygue and Fr\'ed\'eric Jouhet},
     title = {Congruences {Modulo} {Cyclotomic} {Polynomials} and {Algebraic} {Independence} for {q-Series}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a53/}
}
TY  - JOUR
AU  - Boris Adamczewski
AU  - Jason P. Bell
AU  - Éric Delaygue
AU  - Frédéric Jouhet
TI  - Congruences Modulo Cyclotomic Polynomials and Algebraic Independence for q-Series
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a53/
ID  - SLC_2017_78B_a53
ER  - 
%0 Journal Article
%A Boris Adamczewski
%A Jason P. Bell
%A Éric Delaygue
%A Frédéric Jouhet
%T Congruences Modulo Cyclotomic Polynomials and Algebraic Independence for q-Series
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a53/
%F SLC_2017_78B_a53
Boris Adamczewski; Jason P. Bell; Éric Delaygue; Frédéric Jouhet. Congruences Modulo Cyclotomic Polynomials and Algebraic Independence for q-Series. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a53/