Locally Harmonic Maass Forms and the Kernel of the Shintani Lift
Locally Harmonic Maass Forms and the Kernel of the Shintani Lift
复制标题
局部谐波 Maass 形式和 Shintani 电梯的核心
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
W. Kohnen
中科院分区：
文献类型：
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作者：
K. Bringmann;B. Kane;W. Kohnen
在本文中，我们定义了一种新的类型的模块化对象，并构造明确的例子，这样的功能。我们的函数与Zagier [37]构建的尖点形式密切相关，Zagier [37]在Kohnen和Zagier [26]构建半积分和积分权尖点形式之间的Shimura和Shintani提升的核函数中发挥了重要作用。虽然我们的功能有许多共同的性质与调和弱马斯形式，他们也有一些性质，显着对比所表现出的调和弱马斯形式。作为本文所发展的新理论的第一个应用，人们得到了一个新的证明，即Zagier尖点形式的偶数周期是合理的，这是一个简单的推论。
In this paper we define a new type of modular object and construct explicit examples of such functions. Our functions are closely related to cusp forms constructed by Zagier [37] which played an important role in the construction by Kohnen and Zagier [26] of a kernel function for the Shimura and Shintani lifts between half-integral and integral weight cusp forms. Although our functions share many properties in common with harmonic weak Maass forms, they also have some properties which strikingly contrast those exhibited by harmonic weak Maass forms. As a first application of the new theory developed in this paper, one obtains a new proof of the fact that the even periods of Zagier’s cusp forms are rational as an easy corollary.
半积分权调和弱 Maass 形式系数的代数公式
影响因子：
1.7
作者：
J. H. Bruinier;K. Ono
通讯作者：
K. Ono