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Let k = Fq(T) and A = Fq[T]. Fix a prime divisor ℓ of q - 1. In this paper, we consider a ℓ-cyclic real function field k(수식) as a subeldof the imaginary bicyclic function field K = k(수식), which is a composite field of k(수식) with a ℓ-cyclic totally imaginary function field k(수식) of class number one, and give various conditions for the classnumber of k(수식) to be one by using invariants of the relatively cyclicunramied extensions K/Fi over ℓ-cyclic totally imaginary function field Fi = k(수식) for 1≤ i ≤ ℓ-1.
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참고문헌 (10)
참고문헌 신청
C. Wittmann / 2007 / l-class groups of cyclic function fields of degree l / Finite Fields Appl 13 (2) : 327 ~ 347
H. Stichtenoth / 1993 / Algebraic Function Fields and Codes / Springer-Verlag
H. Yokoi / 1967 / On the class number of a relatively cyclic number field / Nagoya Math. J 29 : 31 ~ 34
H. Yokoi / 1986 / Imaginary bicyclic biquadratic fields with the real quadratic subfield of classnumber one / Nagoya Math. J 102 : 91 ~ 100
J. Ahn / 2003 / Cyclotomic units and Stickelberger ideals of global function fields / Trans. Amer. Math. Soc 355 (5) : 1803 ~ 1818
H. Stichtenoth / 1993 / Algebraic Function Fields and Codes / Springer-Verlag
H. Yokoi / 1967 / On the class number of a relatively cyclic number field / Nagoya Math. J 29 : 31 ~ 34
H. Yokoi / 1986 / Imaginary bicyclic biquadratic fields with the real quadratic subfield of classnumber one / Nagoya Math. J 102 : 91 ~ 100
J. Ahn / 2003 / Cyclotomic units and Stickelberger ideals of global function fields / Trans. Amer. Math. Soc 355 (5) : 1803 ~ 1818
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