On Shimura lifting of Hilbert modular forms
On Shimura lifting of Hilbert modular forms
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DOI：
10.1007/s40993-018-0133-y
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发表时间：
2018-09
影响因子：
0.8
通讯作者：
S. Tsuyumine
中科院分区：
文献类型：
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作者：
S. Tsuyumine
设 为完全实数域 K 的可被 4 整除的积分理想。证明了在一定条件下，具有特征模半积分权的希尔伯特模形式空间到具有积分权的希尔伯特模形式空间存在Shimura提升映射。特别是，如果，则任何重量至少为 5 / 2 的希尔伯特模形式都具有 Shimura 升力。作为一个应用，我们计算了and的theta级数的三次方的志村升力，并得到了三个整数平方和的Kas中全正整数的表示数的公式。
Letbe a integral ideal divisible by 4, of a totally real fieldK. We show that there is the Shimura lifting map of a space of Hilbert modular forms with character moduloof half-integral weight, to the space of Hilbert modular forms of integral weight under some condition. In particular it is shown that if, then any Hilbert modular forms of weight at least 5 / 2 has the Shimura lift. As an application, we compute the Shimura lifts of the third powers of theta series forand, and obtain the formulas for the numbers of representations of totally positive integers inKas sums of three integral squares.