Supremum of Random Dirichlet Polynomials with Sub-multiplicative Coefficients

zbMath1313.60071arXiv0904.2316MaRDI QIDQ3083188

Michel J. G. Weber

Publication date: 18 March 2011

Abstract: We study the supremum of random Dirichlet polynomials $D_N(t)=sum_{n=1}^Nvarepsilon_n d(n) n^{- s}$, where $(varepsilon_n)$ 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.

Full work available at URL: https://arxiv.org/abs/0904.2316

zbMATH Keywords

Gaussian processmaximumsub-multiplicative functionindependent Rademacher random variableQueffélec sieve argumentrandom Dirichlet polynomials

Mathematics Subject Classification ID

Gaussian processes (60G15) Dirichlet series, exponential series and other series in one complex variable (30B50)

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