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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
TABOKA P. CHALEBGWA
Journal:

Bulletin of the Australian Mathematical Society / Volume 101 / Issue 3 / June 2020

Published online by Cambridge University Press:

08 October 2019, pp. 415-425

Print publication:

June 2020
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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.