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2020•International Journal of Number TheoryRequires access

Nevanlinna theory and algebraic values of certain meromorphic functions

Taboka Chalebgwa

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Abstract

We extend two results by Boxall and Jones on algebraic values of certain analytic functions to meromorphic functions. We obtain [Formula: see text] bounds for the number of algebraic points of height at most [Formula: see text] on certain restrictions of the graphs of such functions. The constant [Formula: see text] and exponent [Formula: see text] depend on certain data associated with the functions and can be effectively computed from them.

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What this paper is about

We extend two results by Boxall and Jones on algebraic values of certain analytic functions to meromorphic functions. We obtain [Formula: see text] bounds for the number of algebraic points of height at most [Formula: see text] on certain restrictions of the graphs of such functions. The constant [Formula: see text] and exponent [Formula: see text] depend on certain data associated with the functions and can be effectively computed from them.

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Available abstract

We extend two results by Boxall and Jones on algebraic values of certain analytic functions to meromorphic functions. We obtain [Formula: see text] bounds for the number of algebraic points of height at most [Formula: see text] on certain restrictions of the graphs of such functions. The constant [Formula: see text] and exponent [Formula: see text] depend on certain data associated with the functions and can be effectively computed from them.

Key concepts: Meromorphic function, Mathematics, Algebraic number, Exponent, Algebraic function, Pure mathematics, Algebraic cycle, Function field of an algebraic variety

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