Abstract
Let K be a number field, and let G be a finitely generated subgroup of K ×. Fix some positive integer m, and consider the set of primes \(\mathfrak p\) of K satisfying the following condition: the reduction of G modulo \(\mathfrak {p}\) is well-defined and has size coprime to m. We show that the natural density of this set is a computable rational number by reducing to the case where m is prime, case which has been treated in the previous work Reductions of algebraic integers (joint with Christophe Debry, J. Number Theory, 2016).
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References
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Acknowledgements
The author would like to thank Christophe Debry, Franziska Schneider, and Franziska Wutz for their support and the referee for their careful reading of the paper. The project originated as a mentor/mentee collaboration in the WIN style (the mentees left academia).
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Perucca, A. (2018). Reductions of Algebraic Integers II. In: Bouw, I., Ozman, E., Johnson-Leung, J., Newton, R. (eds) Women in Numbers Europe II. Association for Women in Mathematics Series, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-319-74998-3_2
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DOI: https://doi.org/10.1007/978-3-319-74998-3_2
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