PreprintCC BY 4.0arXiv
Local Nevanlinna embedding for Hardy space of Dirichlet series below critical exponent
Abstract
In this paper, we investigate a problem posed by Saksman and Seip [ Contemp. Math., 2016] on whether functions in the Hardy space of Dirichlet series ℋp, 0<p<2, are locally in the Nevanlinna class of the critical half-plane ℂ1/2. We show that the local Nevanlinna embedding fails below critical exponent p=2 by constructing ℋp-functions whose local logarithmic mass becomes unbounded as real s→ 1/2+. This also clarifies the distinction between global Jessen-type logarithmic control and local boundary Nevanlinna behavior for Dirichlet series.
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BibTeX
@misc{allu2026local,
title = {{Local Nevanlinna embedding for Hardy space of Dirichlet series below critical exponent}},
author = {Vasudevarao Allu and Dipon Kumar Mondal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25002},
eprint = {2610.25002},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25002},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Local Nevanlinna embedding for Hardy space of Dirichlet series below critical exponent
AU - Vasudevarao Allu
AU - Dipon Kumar Mondal
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25002
UR - https://arxiv.org/abs/2610.25002
AB - In this paper, we investigate a problem posed by Saksman and Seip [ Contemp. Math., 2016] on whether functions in the Hardy space of Dirichlet series ℋ^p, 0<p<2, are locally in the Nevanlinna class of the critical half-plane ℂ_1/2. We show that the local Nevanlinna embedding fails below critical exponent p=2 by constructing ℋ^p-functions whose local logarithmic mass becomes unbounded as real s→ 1/2^+. This also clarifies the distinction between global Jessen-type logarithmic control and local boundary Nevanlinna behavior for Dirichlet series.
ER -