# Asymptotics of entire functions and a problem of hayman

Hilberdink, T. (2020) Asymptotics of entire functions and a problem of hayman. Quarterly Journal of Mathematics, 71 (2). pp. 667-676. ISSN 0033-5606

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To link to this item DOI: 10.1093/qmathj/haz061

## Abstract/Summary

In this paper we study entire functions whose maximum on a disc of radius $r$ grows like $e^{h(\log r)}$ for some function $h(\cdot)$. We show that this is impossible if $h^{\prime\prime}(r)$ tends to a limit as $r\to\infty$, thereby solving a problem of Hayman from 1966. On the other hand we show that entire functions can, under some mild smoothness conditions, grow like $e^{h(\log r)}$ if $h^{\prime\prime}(r)\to\infty$.

Item Type: Article Yes Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics 88558 Oxford University Press

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