Weil numbers in finite extensions of ℚ
            ab: The Loxton-Kedlaya phenomenon

Florin Stan; Alexandru Zaharescu

doi:10.1090/s0002-9947-2014-06414-3

Weil numbers in finite extensions of ℚ ^ab: The Loxton-Kedlaya phenomenon

Florin Stan, Alexandru Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

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 ℚ ^ab. In the present paper we show that this phenomenon extends to all finite extensions of ℚ ^ab.

Original language	English (US)
Pages (from-to)	4359-4376
Number of pages	18
Journal	Transactions of the American Mathematical Society
Volume	367
Issue number	6
DOIs	https://doi.org/10.1090/s0002-9947-2014-06414-3
State	Published - 2015

Keywords

Cyclotomic fields
Weil numbers

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Online availability

10.1090/s0002-9947-2014-06414-3

Library availability

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Cite this

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title = "Weil numbers in finite extensions of ℚ ab: The Loxton-Kedlaya phenomenon",

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 ℚ ab. In the present paper we show that this phenomenon extends to all finite extensions of ℚ ab. ",

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KW - Weil numbers

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