RADIAL ASYMPTOTICS OF GENERATING FUNCTIONS OF <i>k</i>-REGULAR SEQUENCES

Abstract We give a new proof of a theorem of Bell and Coons [‘Transcendence tests for Mahler functions’, Proc. Amer. Math. Soc. 145 (3) (2017), 1061–1070] on the leading order radial asymptotics of Mahler functions that are the generating functions of regular sequences. Our method allows us to provide a description of the oscillations whose existence was shown by Bell and Coons. This extends very recent results of Poulet and Rivoal [‘Radial behavior of Mahler functions’, Int. J. Number Theory , to appear].