ON THE ORDER OF MAGNITUDE OF SUDLER PRODUCTS.

Given an irrational number α ∈ (0,1), the Sudler product is defined by P_N (α) = QN_r=1 2|sinπrα|. Answering a question of Grepstad, Kaltenbock and Neumüller we prove aöasymptotic formula for distorted Sudler products when α is the golden ratio ( √ 5+1)/2 and establish that in this case limsup _N→∞ PN (α)/_{N < ∞}. We obtain similar results for quadratic irrationals α with continued fraction expansion α = [a,a,a,...] for some integer a ≥ 1, and give a full characterisation of the values of a for which liminf _N→∞ PN (α) > 0 and limsup _N→∞ PN (α)/ _{N < ∞} hold, respectively. We establish that there is a (sharp) transition point at a = 6, and resolve as a by-product a problem of the first author, Larcher, Pillichshammer, Saad Eddin, and Tichy. [ABSTRACT FROM AUTHOR]