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ALGEBRAIC VALUES OF CERTAIN ANALYTIC FUNCTIONS DEFINED BY A CANONICAL PRODUCT

Part of: Entire and meromorphic functions, and related topics Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  08 October 2019

TABOKA P. CHALEBGWA Open the ORCID record for TABOKA P. CHALEBGWA [Opens in a new window]
TABOKA P. CHALEBGWA*
Affiliation:
The Fields Institute, 222 College Street, 3rd Floor, Toronto, Ontario M5T 3J1, Canada email taboka@aims.ac.za Department of Mathematical Sciences, Mathematics Division, Stellenbosch University, Private Bag X1, 7602 Matieland, South Africa
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Abstract

We give a partial answer to a question attributed to Chris Miller on algebraic values of certain transcendental functions of order less than one. We obtain $C(\log H)^{\unicode[STIX]{x1D702}}$ bounds for the number of algebraic points of height at most $H$ on certain subsets of the graphs of such functions. The constant $C$ and exponent $\unicode[STIX]{x1D702}$ depend on data associated with the functions and can be effectively computed from them.

Keywords

algebraic pointsbounded heighttranscendental functions

MSC classification

Primary: 11J99: None of the above, but in this section
Secondary: 30D20: Entire functions, general theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 3 , June 2020 , pp. 415 - 425
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

This work is based on the research supported in part by the National Research Foundation of South Africa (Grant Number 96234). The author was also supported by the South African National Research Foundation Innovation doctoral scholarship and a Fields-AIMS-Perimeter postdoctoral scholarship.

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