Zeros of Functions in Bergman-Type Hilbert Spaces of Dirichlet Series

  • Ole Fredrik Brevig

Abstract

For a real number $\alpha$ the Hilbert space $\mathscr{D}_\alpha$ consists of those Dirichlet series $\sum_{n=1}^\infty a_n/n^s$ for which $\sum_{n=1}^\infty |a_n|^2/[d(n)]^\alpha < \infty$, where $d(n)$ denotes the number of divisors of $n$. We extend a theorem of Seip on the bounded zero sequences of functions in $\mathscr{D}_\alpha$ to the case $\alpha>0$. Generalizations to other weighted spaces of Dirichlet series are also discussed, as are partial results on the zeros of functions in the Hardy spaces of Dirichlet series $\mathscr{H}^p$, for $1\leq p <2$.
Published
2016-11-01
How to Cite
Brevig, O. F. (2016). Zeros of Functions in Bergman-Type Hilbert Spaces of Dirichlet Series. MATHEMATICA SCANDINAVICA, 119(2), 237-248. https://doi.org/10.7146/math.scand.a-24745
Section
Articles