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

Florin Stan, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)4359-4376
Number of pages18
JournalTransactions of the American Mathematical Society
Issue number6
StatePublished - 2015


  • Cyclotomic fields
  • Weil numbers

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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