Zeros of Functions in Bergman-Type Hilbert Spaces of Dirichlet Series - Brevig, Ole Fredrik (Mathematica Scandinavica, 2016)
For a real number $α$ the Hilbert space $\mathscr{D}_α$ consists of those Dirichlet series $\sum_{n=1}^∞ a_n/n^s$ for which $\sum_{n=1}^∞ |a_n|^2/[d(n)]^α < ∞$, where $d(n)$ denotes the number of divisors of $n$. We extend a theorem of Seip on the bounded zero sequences of functions in $\mathscr{D}_α$ to the case $α>0$. 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≤ p