# Algebraic values of certain analytic functions defined by a canonical product

## TL;DR

This paper investigates the algebraic values of specific transcendental functions of order less than one, providing bounds on the number of algebraic points of bounded height on their graphs, with effective constants.

## Contribution

It offers a partial answer to a question about algebraic values of these functions and derives explicit bounds depending on computable data.

## Key findings

- Established bounds of C(logH)^n for algebraic points on function graphs
- Constants and exponents are effectively computable from function data
- Addresses a question attributed to Chris Miller

## 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(logH)^n 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 n depend on certain data associated with the functions and can be effectively computed from them.