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We apply the character sums method of Lenstra, Moree, and Stevenhagen, toexplicitly compute the constants in the Titchmarsh divisor problem for Kummerfields and for division fields of Serre curves. We derive our results asspecial cases of a general result on the product expressions for the sums inthe form $$\sum_{n=1}^{\infty}\frac{g(n)}{\#G(n)}$$ in which $g(n)$ is amultiplicative arithmetic function and $\{G(n)\}$ is a certain family of Galoisgroups. Our results extend the application of the character sums method to theevaluation of constants, such as the Titchmarsh divisor constants, that are notdensity constants.

Constants for Artin like problems in Kummer and division fields