Siegel Paramodular Forms from Exponential Lifts: Slow versus Fast Growth
Siegel Paramodular Forms from Exponential Lifts: Slow versus Fast Growth
复制标题
指数提升的西格尔副模形式：缓慢增长与快速增长
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Beatrix Muhlmann
中科院分区：
文献类型：
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作者：
Alexandre Belin;A. Castro;C. Keller;Beatrix Muhlmann
我们调查的增长的Siegel paramodular形式建立指数提升弱Jacobi形式的傅立叶系数，专注于大的负判别式。为此，我们实现了一种方法的基础上变形的轮廓，表示所有这些条款的系数作为残留物。我们发现，有两种类型的弱雅可比形式，导致两种不同的增长行为：更常见的类型导致快速，指数增长，而第二种类型导致较慢的增长，类似于theta函数的比率增长。我们给出了一个简单的标准来区分这两种类型，并给出了一个简单的封闭形式的表达式的系数在缓慢增长的情况下。在另一篇文章[1]中，我们将这些结果应用于对称乘积轨道和全息。
We investigate the growth of Fourier coefficients of Siegel paramodular forms built by exponentially lifting weak Jacobi forms, focusing on terms with large negative discriminant. To this end we implement a method based on deforming contours that expresses the coefficients of all such terms as residues. We find that there are two types of weak Jacobi forms, leading to two different growth behaviors: the more common type leads to fast, exponential growth, whereas a second type leads to slower growth, akin to the growth seen in ratios of theta functions. We give a simple criterion to distinguish between the two types, and give a simple closed form expression for the coefficients in the slow growing case. In a companion article [1], we provide physical applications of these results to symmetric product orbifolds and holography.