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Algebraic Values of Entire Functions with Extremal Growth Orders: An Extension of a Theorem of Boxall and Jones

Published online by Cambridge University Press:  15 October 2019

Taboka Prince Chalebgwa
Taboka Prince Chalebgwa*
Affiliation:
Fields Institute, 222 College St, 3rd Floor, M5T 3J1, Toronto, Canada Department of Mathematical Sciences, Mathematics Division, Stellenbosch University, Private Bag X1, 7602 Matieland, South Africa Email: [email protected]
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Abstract

Given an entire function $f$ of finite order $\unicode[STIX]{x1D70C}$ and positive lower order $\unicode[STIX]{x1D706}$, Boxall and Jones proved a bound of the form $C(\log H)^{\unicode[STIX]{x1D702}(\unicode[STIX]{x1D706},\unicode[STIX]{x1D70C})}$ for the density of algebraic points of bounded degree and height at most $H$ on the restrictions to compact sets of the graph of $f$. The constant $C$ and exponent $\unicode[STIX]{x1D702}$ are effectively computable from certain data associated with the function. In this followup note, using different measures of the growth of entire functions, we obtain similar bounds for other classes of functions to which the original theorem does not apply.

Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 3 , September 2020 , pp. 536 - 546
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Copyright
© Canadian Mathematical Society 2019

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Footnotes

This article was completed under the Fields-AIMS-Perimeter postdoctoral fellowship, provided by the Fields Institute for Research in Mathematical Sciences.

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