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Determinant formulas for class numbers in function fields
Author(s):
Hwanyup
Jung;
Sunghan
Bae;
Jaehyun
Ahn.
Journal:
Math. Comp.
74
(2005),
953-965.
MSC (2000):
Primary 11R58, 11R60
Posted:
May 24, 2004
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Abstract:
In this paper, by extending Kucera's idea to the function field case, we obtain several determinant formulas involving the real class number and the relative class number of any subfield of cyclotomic function fields. We also provide several examples using these determinant formulas.
References:
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- 1.
- J. Ahn, S. Bae and H. Jung, Cyclotomic units and Stickelberger ideals of global function fields. Trans. Amer. Math. Soc. 355 (2003), no. 5, 1803-1818.
- 2.
- S. Bae, H. Jung and J. Ahn, Class numbers of some abelian extensions of rational function fields. Math. Comp. 73 (2004), no. 245, 377-386.
- 3.
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- 5.
- F. Harrop, Circular units of function fields. Trans. Amer. Math. Soc. 341 (1994), 405-421. MR 94c:11106
- 6.
- H. Jung and J. Ahn, On the relative class number of cyclotomic function fields. Acta Arith. 107 (2003), no. 1, 91-101. MR 2003j:11143
- 7.
- H. Jung and J. Ahn, Demjanenko matrix and recursion formula for relative class number over function fields. J. Number Theory 98 (2003), no. 1, 55-66. MR 2003i:11170
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Additional Information:
Hwanyup
Jung
Affiliation:
Department of Mathematics Education, Chungbuk National University, Cheongju, Chungbuk, South Korea 361-763
Email:
hyjung@chungbuk.ac.kr
Sunghan
Bae
Affiliation:
Department of Mathematics, KAIST, Daejon, South Korea 305-701
Email:
shbae@math.kaist.ac.kr
Jaehyun
Ahn
Affiliation:
Department of Mathematics, Chungnam National University, Daejon, South Korea 305-764
Email:
jhahn@cnu.ac.kr
DOI:
10.1090/S0025-5718-04-01671-0
PII:
S 0025-5718(04)01671-0
Received by editor(s):
July 18, 2002
Received by editor(s) in revised form:
October 1, 2003
Posted:
May 24, 2004
Additional Notes:
This work was supported by grant No. R01-2002-000-00151-0 from the Basic Research Program of the Korea Science and Engineering Foundation
Copyright of article:
Copyright
2004,
American Mathematical Society
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