Abstract
Consider a one-dimensional torus defined over a number field, and fix a finitely generated group of rational points. How often is the size of the reduction of this group coprime to some given (square-free) integer? In this short note, we prove a formula that allows us to reduce to the case of a prime number.
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References
D. Lombardo, A. Perucca, Reductions of points on algebraic groups, arXiv:1612.02847
A. Perucca, Reductions of algebraic integers II, in Women in Numbers Europe II: Contributions to Number Theory and Arithmetic Geometry, ed. by I. I. Bouw, E. Ozman, J. Johnson-Leung, R. Newton. Association for Women in Mathematics Series, vol. 11, 1st edn. (Springer, New York, 2018). https://doi.org/10.1007/978-3-319-74998-3_2
A. Perucca, Reductions of one-dimensional tori. Int. J. Number Theory 13(6), 1473–1489 (2017)
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Perucca, A. (2018). Reductions of One-Dimensional Tori 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_3
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DOI: https://doi.org/10.1007/978-3-319-74998-3_3
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