On the law of the iterated logarithm for random exponential sums

Research output: Contribution to journalArticlepeer-review


The asymptotic behavior of exponential sums N k=1 exp(2πin k α) for Hadamard lacunary (n k ) is well known, but for general (n k ) very few precise results exist, due to number theoretic difficulties. It is therefore natural to consider random∑ (n k ), and in this paper we prove the law of the iterated logarithm for N k=1 exp(2πin k α) if the gaps n k+1 −n k are independent, identically distributed random variables. As a comparison, we give a lower bound for the discrepancy of {n k α} under the same random model, exhibiting a completely different behavior.

Original languageEnglish
Pages (from-to)3259-3280
Number of pages22
JournalTransactions of the American Mathematical Society
Issue number5
Publication statusPublished - 1 May 2019

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this