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1 results

Improved Bloch and Landau constants for meromorphic functions
Part of
- Entire and meromorphic functions, and related topics
Bappaditya Bhowmik, Sambhunath Sen
Journal:

Canadian Mathematical Bulletin / Volume 66 / Issue 4 / December 2023

Published online by Cambridge University Press:

28 April 2023, pp. 1269-1273

Print publication:

December 2023
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Let ${\mathbb D}$ be the open unit disk, and let $\mathcal {A}(p)$ be the class of functions f that are holomorphic in ${\mathbb D}\backslash \{p\}$ with a simple pole at $z=p\in (0,1)$, and $f'(0)\neq 0$. In this article, we significantly improve lower bounds of the Bloch and the Landau constants for functions in ${\mathcal A}(p)$ which were obtained in Bhowmik and Sen (2023, Monatshefte für Mathematik, 201, 359–373) and conjecture on the exact values of such constants.