Arithmetic properties of coefficients of half-integral weight Maass–Poincaré series
Arithmetic properties of coefficients of half-integral weight Maass–Poincaré series
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半积分权Maass-Poincaré级数系数的算术性质
DOI：
10.1007/s00208-006-0048-0
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发表时间：
2007
影响因子：
1.4
通讯作者：
K. Ono
中科院分区：
文献类型：
--
作者：
K. Bringmann;K. Ono
Zagier [23]证明了1阶奇异模迹的生成函数是权3/2模形式。他还获得了推广的“扭曲的痕迹”，并为痕迹的特殊非全纯模函数。利用Kloosterman-Salié和的性质，以及Salié和在CM点轨道上的一个著名的重新表述，系统地证明了在Kohnen的Γ0（4）+空间中，这样的结果对任意弱全纯和尖点半整权Poincaré级数都成立.这些结果暗示了Zagier的上述结果，并提供了这种迹线的精确公式。
Zagier [23] proved that the generating functions for the traces of level 1 singular moduli are weight 3/2 modular forms. He also obtained generalizations for “twisted traces”, and for traces of special non-holomorphic modular functions. Using properties of Kloosterman-Salié sums, and a well known reformulation of Salié sums in terms of orbits of CM points, we systematically show that such results hold for arbitrary weakly holomorphic and cuspidal half-integral weight Poincaré series in Kohnen’s Γ0(4) plus-space. These results imply the aforementioned results of Zagier, and they provide exact formulas for such traces.