2013年2月
ENDOSCOPIC LIFTS TO THE SIEGEL MODULAR THREEFOLD RELATED TO KLEIN'S CUBIC THREEFOLD
AMERICAN JOURNAL OF MATHEMATICS
- ,
- 巻
- 135
- 号
- 1
- 開始ページ
- 183
- 終了ページ
- 205
- 記述言語
- 英語
- 掲載種別
- DOI
- 10.1353/ajm.2013.0002
- 出版者・発行元
- JOHNS HOPKINS UNIV PRESS
Let A(11)(lev) be the moduli space of (1, 11)-polarized abelian surfaces with a canonical level structure. Let x be a primitive character of order 5 with conductor 11. In this paper we construct five endoscopic lifts Pi(i), 0 <= i <= 4 from two elliptic modular forms f circle times x(i) of weight 2 and g circle times x(i) of weight 4 with complex multiplication by Q(root-11) such that Pi(i infinity) gives a non-holomorphic differential form on A(11)(lev) for each i, 0 <= i <= 4. Then their spinor L-functions are of form L(s - 1, f circle times x(i))L(s,g circle times x(i)) such that L(s,g circle times x(i)) does not appear in the L-function of A(11)(lev) for any i, 0 <= i <= 4. The existence of such lifts is motivated by the computation of the L-function of Klein's cubic threefold which is a birational smooth model of A(11)(lev).
- リンク情報
- ID情報
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- DOI : 10.1353/ajm.2013.0002
- ISSN : 0002-9327
- Web of Science ID : WOS:000320010500009