Weil numbers in finite extensions of $\mathbb {Q}^{ab}$: the Loxton-Kedlaya phenomenon
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- by Florin Stan and Alexandru Zaharescu; with an appendix by Kiran S. Kedlaya PDF
- Trans. Amer. Math. Soc. 367 (2015), 4359-4376 Request permission
Abstract:
A finiteness phenomenon described by Loxton and later by Kedlaya states that, for any fixed $m$, there exist (modulo multiplication by roots of unity) only finitely many $m$-Weil numbers in $\mathbb {Q}^{ab}$. In the present paper we show that this phenomenon extends to all finite extensions of $\mathbb {Q}^{ab}$.References
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Additional Information
- Florin Stan
- Affiliation: Simion Stoilow Institute of Mathematics of the Romanian Academy, Research unit 5, PO Box 1-764, RO-014700 Bucharest, Romania
- Email: sfloringabriel@yahoo.com
- Alexandru Zaharescu
- Affiliation: Simion Stoilow Institute of Mathematics of the Romanian Academy, Research unit 5, PO Box 1-764, RO-014700 Bucharest, Romania — and — Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, Illinois 61801
- MR Author ID: 186235
- Email: zaharesc@illinois.edu
- Kiran S. Kedlaya
- MR Author ID: 349028
- ORCID: 0000-0001-8700-8758
- Received by editor(s): September 18, 2012
- Received by editor(s) in revised form: August 21, 2013
- Published electronically: November 18, 2014
- Additional Notes: The research of the second author was supported by the NSF grant DMS-0901621.
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 367 (2015), 4359-4376
- MSC (2010): Primary 11R18, 11R06
- DOI: https://doi.org/10.1090/S0002-9947-2014-06414-3
- MathSciNet review: 3324931