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- W4301258154 abstract "Conditionally on the Generalized Riemann Hypothesis (GRH), we prove the following results: (1) a cyclic number field of degree $5$ is norm-Euclidean if and only if $Delta=11^4,31^4,41^4$; (2) a cyclic number field of degree $7$ is norm-Euclidean if and only if $Delta=29^6,43^6$; (3) there are no norm-Euclidean cyclic number fields of degrees $19$, $31$, $37$, $43$, $47$, $59$, $67$, $71$, $73$, $79$, $97$. Our proofs contain a large computational component, including the calculation of the Euclidean minimum in some cases; the correctness of these calculations does not depend upon the GRH. Finally, we improve on what is known unconditionally in the cubic case by showing that any norm-Euclidean cyclic cubic field must have conductor $fleq 157$ except possibly when $fin(2cdot 10^{14}, 10^{50})$." @default.
- W4301258154 created "2022-10-05" @default.
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- W4301258154 date "2016-01-13" @default.
- W4301258154 modified "2023-09-27" @default.
- W4301258154 title "The Euclidean algorithm in quintic and septic cyclic fields" @default.
- W4301258154 doi "https://doi.org/10.48550/arxiv.1601.03433" @default.
- W4301258154 hasPublicationYear "2016" @default.
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