Cuspidal class number of the tower of modular curves X
1(Np
n
) |
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Authors: | Hae-Sang Sun |
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Institution: | 1. Max-Planck Institut für Mathematik Bonn, Vivatsgasse 7, 53111, Bonn, Germany 2. Korea Institute for Advanced Study, Hoegiro 87, Dongdaemun-gu, Seoul, 130-722, Korea
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Abstract: | We consider a cuspidal class number, which is the order of a subgroup of the full cuspidal divisor class group of X
1(Np
n
) with
p\nmid N{p\nmid N} and n ≥ 1. By studying the second generalized Bernoulli numbers, we obtain results similar to ones (Ferrero and Washington in Ann
Math (2) 109(2):377–395, 1979; Washington in Invent Math 49:87–97, 1978) about the relative class numbers of cyclotomic
\mathbbZp{\mathbb{Z}_p}-extension of an abelian number field. |
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Keywords: | |
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