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GROUP DETERMINANT FORMULAS AND CLASS NUMBERS OF CYCLOTOMIC FIELDS
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 Title & Authors
GROUP DETERMINANT FORMULAS AND CLASS NUMBERS OF CYCLOTOMIC FIELDS
Jung, Hwan-Yup; Ahn, Jae-Hyun;
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 Abstract
Let m, n be positive integers or monic polynomials in with n|m. Let be the m-th cyclotomic field and its maximal real subfield, respectively. In this paper we define two matrices whose determinants give us the ratios and with some factors, respectively.
 Keywords
cyclotomic unit;cyclotomic function field;
 Language
English
 Cited by
1.
ON THE RATIO OF RELATIVE CONGRUENCE ZETA FUNCTIONS OF CYCLOTOMIC FUNCTION FIELDS, Journal of the Chungcheong Mathematical Society , 2016, 29, 1, 117  crossref(new windwow)
 References
1.
J. Ahn, S. Choi, and H. Jung, Class number formulas in the form of a product of determinants in function fields, J. Aust. Math. Soc. 78 (2005), no. 2, 227-238 crossref(new window)

2.
S. Galovich and M. Rosen, Units and class groups in cyclotomic function fields, J. Number Theory 14 (1982), no. 2, 156-184 crossref(new window)

3.
K. Girstmair, A recursion formula for the relative class number of the -th cyclotomic field, Abh. Math. Sem. Univ. Hamburg 61 (1991), 131-138 crossref(new window)

4.
H. J ung and J. Ahn, Demjanenko matrix and recursion formula for relative class number over function fields, J. Number theory 98 (2003), no. 1, 55-66 crossref(new window)

5.
H. Jung, S. Bae, and J. Ahn, Determinant formulas for class numbers in function fields, Math. Comp. 74 (2005), no. 250, 953-965 crossref(new window)

6.
R. Kucera, Formulae for the relative class number of an imaginary abelian field in the form of a determinant, Nagoya Math. J. 163 (2001), 167-191

7.
M. Rosen, The Hilbert class field in function fields, Exposition. Math. 5 (1987), no. 4, 365-378

8.
M. Rosen, Number theory in function fields, Graduate Texts in Mathematics 210, Springer-Verlag, New York, 2002

9.
L. Washington, Introduction to cyclotomic fields. Second edition, Graduate Texts in Mathematics 83, Springer-Verlag, New York, 1997

10.
L. Yin, On the index of cyclotomic units in characteristic p and its applications, J. Number Theory 63 (1997), no. 2, 302-324 crossref(new window)

11.
L. Yin, Distributions on a global field, J. Number Theory 80 (2000), no. 1, 154-167 crossref(new window)

12.
L. Yin, Stickelberger ideals and relative class numbers in function fields, J. Number Theory 81 (2000), no. 1, 162-169 crossref(new window)