THE SIZE OF (q; q)n FOR q ON THE UNIT CIRCLE

@inproceedings{Lubinsky2006THESO,
  title={THE SIZE OF (q; q)n FOR q ON THE UNIT CIRCLE},
  author={Doron S. Lubinsky},
  year={2006}
}
There is increasing interest in q series with jqj = 1. In analysis of these, an important role is played by the behaviour as n!1 of (q; q)n = (1 q)(1 q):::(1 q): We show, for example, that for almost all q on the unit circle log j(q; q)nj = O(logn) i¤ " > 0. Moreover, if q = exp(2 i ) where the continued fraction of has bounded partial quotients, then the above relation is valid with " = 0. This provides an interesting contrast to the well known geometric growth as n!1 of k (q; q)n kL1(jqj=1… CONTINUE READING