Abstract
Let L be a finite extension of \(\mathbb {F}_q(t)\). We calculate the proportion of polynomials of degree d in \(\mathbb {F}_q[t]\) that are everywhere locally norms from \(L/\mathbb {F}_q(t)\) which fail to be global norms from \(L/\mathbb {F}_q(t)\).
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Acknowledgements
This project began at the Women in Numbers Europe 3 workshop in August 2019. We are grateful to the organisers for bringing us together and to the Henri Lebesgue Center for providing us with an excellent working environment to get this project underway. We thank Alp Bassa, Titus Hilberdink, Yiannis Petridis and Efthymios Sofos for useful discussions. We are grateful to the anonymous referee for useful feedback which improved the paper. Magma [4] was used to investigate examples. Rachel Newton was supported by EPSRC grant EP/S004696/1 and UKRI Future Leaders Fellowship MR/T041609/1. Ekin Ozman conducted part of this research while she was at MPIM-Bonn and would like to express her gratitude for excellent working conditions.
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Mânzăţeanu, A., Newton, R., Ozman, E., Sutherland, N., Uysal, R.G. (2021). The Hasse Norm Principle in Global Function Fields. In: Cojocaru, A.C., Ionica, S., García, E.L. (eds) Women in Numbers Europe III. Association for Women in Mathematics Series, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-030-77700-5_9
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