### Abstract

We discuss algebraic Γ-monomials of Deligne. Deligne used the theory of Hodge Cycles to show that algebraic Γ-monomials generate Kummer extensions of certain cyclotomic fields. Das, using a double complex of Anderson and Deligne's results, showed that certain powers of algebraic Γ-monomials and certain square roots of sine monomials generate abelian extensions of ℚ. Das also gave one example of a nonabelian double covering of a cyclotomic field generated by the square root of a sine monomial. In this note, we will produce infinitely many examples of non-abelian double coverings of cyclotomic fields of Das type. The construction of the examples depends in an interesting way on a lemma of Gauss figuring in an elementary proof of quadratic reciprocity.

Original language | English |
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Pages (from-to) | 76-85 |

Number of pages | 10 |

Journal | Journal of Number Theory |

Volume | 93 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2002 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory