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 タイトル: Gross'Conjecture for Extensions Ramified over Three Points of $\Bbb P^1$ 著者: Reid, Michael 発行日: 2003年 出版者: Graduate School of Mathematical Sciences, The University of Tokyo 掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 10 (2003), No. 1, Page 119-138 抄録: B. Gross has formulated a conjectural generalization of the class number formula. Suppose $L/K$ is an abelian extension of global fields with Galois group $G$. A generalized Stickelberger element $θ \in \ZZ[G]$ is constructed from special values of $L$-functions at $s = 0$. Gross'conjecture then predicts some $I$-adic information about $θ$, where $I \subseteq \ZZ[G]$ is the augmentation ideal. In this paper, we prove (under a mild hypothesis) the conjecture for the maximal abelian extension of the rational function field $\FF_q(X)$ that is unramified outside a set of three degree $1$ places. URI: http://hdl.handle.net/2261/43961 ISSN: 13405705 出現カテゴリ: Journal of Mathematical Sciences, the University of TokyoJournal of Mathematical Sciences, the University of Tokyo

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