Supremum of Random Dirichlet Polynomials with Sub-multiplicative Coefficients

Abstract

We study the supremum of random Dirichlet polynomials $D_N(t)={\sum }_{n=1}^N{\epsilon }_{n}d(n)n^{-s}$, where $({\epsilon }_n)$ is a sequence of independent Rademacher random variables, and $d$ is a sub-multiplicative function. The approach is gaussian and entirely based on comparison properties of Gaussian processes, with no use of the metric entropy method.

28pages

References in corpus (1)

• On localization in Kronecker's diophantine theorem

Cited by in corpus (1)

• Dirichlet polynomials: some old and recent results, and their interplay in number theory