On formulas for the index of the circular distributions |
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Authors: | Soogil Seo |
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Institution: | (1) Department of Mathematics, Yonsei University, 134 Sinchon-Dong, Seodaemun-Gu, Seoul, 120-749, South Korea |
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Abstract: | A circular distribution is a Galois equivariant map ψ from the roots of unity μ
∞ to an algebraic closure of such that ψ satisfies product conditions, for ϵ ∈ μ
∞ and , and congruence conditions for each prime number l and with (l, s) = 1, modulo primes over l for all , where μ
l
and μ
s
denote respectively the sets of lth and sth roots of unity. For such ψ, let be the group generated over by and let be , where U
s
denotes the global units of . We give formulas for the indices and of and inside the circular numbers P
s
and units C
s
of Sinnott over .
This work was supported by the SRC Program of Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government
(MOST) (No. R11-2007-035-01001-0). This work was supported by the Korea Research Foundation Grant funded by the Korean Government
(MOEHRD, Basic Research Promotion Fund) (KRF-2006-312-C00455). |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 11R18 11S23 11R27 11R29 11S31 11R34 11R37 |
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