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A Shintani-type formula for Gross--Stark units over function fields
http://hdl.handle.net/2261/38188
http://hdl.handle.net/2261/3818807f200e2-348e-47b8-9318-be05a91d76a4
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms160302.pdf (223.1 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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| 公開日 | 2010-11-30 | |||||
| タイトル | ||||||
| タイトル | A Shintani-type formula for Gross--Stark units over function fields | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | asymptotic | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | behavior | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| 著者 |
Dasgupta, Samit
× Dasgupta, Samit× Miller, Alison |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | Let F be a totally real number field of degree n, and let H be a finite abelian extension of F. Let p denote a prime ideal of F that splits completely in H. Following Brumer and Stark, Tate conjectured the existence of a p-unit u in H whose p-adic absolute values are related in a precise way to the partial zeta-functions of the extension H/F. Gross later refined this conjecture by proposing a formula for the p-adic norm of the element u. Recently, using methods of Shintani, the first author refined the conjecture further by proposing an exact formula for u in the p-adic completion of H. In this article we state and prove a function field analogue of this Shintani-type formula. The role of the totally real field F is played by the function field of a curve over a finite field in which n places have been removed. These places represent the “real places” of F. Our method of proof follows that of Hayes, who proved Gross’s conjecture for function fields using the theory of Drinfeld modules and their associated exponential functions. | |||||
| 書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 16, 号 3, p. 415-440, 発行日 2009-11-30 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 13405705 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA11021653 | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 415 | |||||
| Mathematical Reviews Number | ||||||
| MR | ||||||
| Mathmatical Subject Classification | ||||||
| 11R58(MSC2000) | ||||||
| Mathmatical Subject Classification | ||||||
| 11R37(MSC2000) | ||||||
| Mathmatical Subject Classification | ||||||
| 11R80(MSC2000) | ||||||
| Mathmatical Subject Classification | ||||||
| 11G09(MSC2000) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 2008-08-25 | ||||||
