The asymptotic oscillations of moments related to Dirichlet series with missing digits

TL;DR

This paper demonstrates that moments of measures linked to Dirichlet series with missing digits exhibit asymptotic 1-periodic oscillations in the base b logarithm of the index.

Contribution

It establishes the asymptotic periodicity of moments related to Dirichlet series with missing digits in radix b.

Findings

Moments are asymptotically invariant under multiplication by b.

The oscillations are 1-periodic in the base b logarithm.

Results connect digit missing patterns to Dirichlet series behavior.

Abstract

We prove that the (suitably rescaled) moments of certain discrete measures on the unit interval, which are related to the numerical evaluation of zeta series with missing digits in radix $b$, are asymptotically $1$-periodic in the base $b$ logarithm of the index, i.e. asymptotically invariant under multiplication by $b$ of the index.