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このアイテムのファイル:
ファイル | 記述 | サイズ | フォーマット | |
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2014-05.pdf | 1.15 MB | Adobe PDF | 見る/開く |
タイトル: | NOTES ON LOW DEGREE L-DATA (Analytic Number Theory and Related Areas) |
著者: | Oliver, Thomas |
発行日: | Jan-2017 |
出版者: | 京都大学数理解析研究所 |
誌名: | 数理解析研究所講究録 |
巻: | 2014 |
開始ページ: | 48 |
終了ページ: | 58 |
抄録: | These notes are an extended version of a talk given by the author at the conference Analytic Number Theory and Related Areas held at Research Institute for Mathematical Sciences, Kyoto University in November 2015. We are interested in L-data , an axiomatic framework for Lsim-functions introduced by Andrew Booker in 2013 [3]. Associated to each L-datum, one has a real number invariant known as the degree. Conjecturally the degree d is an integer, and if din mathrm{N} then the L-datum is that of a mathrm{G}mathrm{L}_{n}(mathrm{A}_{F})-automorphic representation for nin mathrm{N} and a number field F (if F=mathbb{Q}, then n=d This statement was shown to be true for 0displaystyle leq d<frac{5}{3} by Booker in his pioneering paper [3], and in these notes we consider an extension of his methods to 0leq d<2 . This is simultaneously a generalisation of Booker s result and the results and techniques of Kaczorowski-Pereli in the Selberg class [10]. Furthermore, we consider applications to zeros of automorphic L-functions. In these notes we review Booker s results and announce new ones to appear elsewhere shortly [11]. |
URI: | http://hdl.handle.net/2433/231651 |
出現コレクション: | 2014 解析的整数論とその周辺 |
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