Limit theorems for random Dirichlet series: boundary case

2024/11/04 by Iksanov, Alexander, Kostohryz, Ruslan · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2411.02362

Abstract

Buraczewski et al (2023) proved a functional limit theorem (FLT) and a law of the iterated logarithm (LIL) for a random Dirichlet series ∑_{k≥ 2}(log k)^αk^-1/2-sη_k as s→ 0+, where α>-1/2 and η₁, η₂,… are independent identically distributed random variables with zero mean and finite variance. We prove a FLT and a LIL in a boundary case α=-1/2. The boundary case is more demanding technically than the case α>-1/2.

Cited by

• Limit theorems for random Dirichlet series with summation over primes, with an application to Rademacher random multiplicative functions

Related

• Limit theorems for random Dirichlet series with summation over primes, with an application to Rademacher random multiplicative functions
• Limit theorems for random Dirichlet series
• Precise tail behavior of some Dirichlet series
• On Random Multiple Dirichlet Series
• How many real zeros does a random Dirichlet series have?