On the law of the iterated logarithm for random exponential sums

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

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.

Originalspracheenglisch
Seiten (von - bis)3259-3280
Seitenumfang22
FachzeitschriftTransactions of the American Mathematical Society
Jahrgang371
Ausgabenummer5
DOIs
PublikationsstatusVeröffentlicht - 1 Mai 2019
Extern publiziertJa

ASJC Scopus subject areas

  • !!Mathematics(all)
  • Angewandte Mathematik

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