### 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 |
---|---|

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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

}

*Journal of Number Theory*, vol. 93, no. 1, pp. 76-85. https://doi.org/10.1006/jnth.2001.2714

**A note on algebraic λc-monomials and double coverings.** / Seo, Soogil.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A note on algebraic λc-monomials and double coverings

AU - Seo, Soogil

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0036222249&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036222249&partnerID=8YFLogxK

U2 - 10.1006/jnth.2001.2714

DO - 10.1006/jnth.2001.2714

M3 - Article

AN - SCOPUS:0036222249

VL - 93

SP - 76

EP - 85

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -