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arXiv · 1907.12323

Henry Helson meets other big shots -- A brief survey

Andreas Defant·Ingo Schoolmann
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Abstract

A theorem of Henry Helson shows that for every ordinary Dirichlet series $\sum a_n n^{-s}$ with a square summable sequence $(a_n)$ of coefficients, almost all vertical limits $\sum a_n \chi(n) n^{-s}$, where $\chi: \mathbb{N} \to \mathbb{T}$ is a completely multiplicative arithmetic function, converge on the right half-plane. We survey on recent improvements and extensions of this result within Hardy spaces of Dirichlet series -- relating it with some classical work of Bohr, Banach, Carleson-Hunt, Ces\`{a}ro, Hardy-Littlewood, Hardy-Riesz, Menchoff-Rademacher, and Riemann.

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Andreas Defant, Ingo Schoolmann. 2019-07-29. Henry Helson meets other big shots -- A brief survey. https://arxiv.org/abs/1907.12323

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