Spectral zeta function on pseudo H-type nilmanifolds
Spectral zeta function on pseudo H-type nilmanifolds
复制标题
伪 H 型尼尔流形的光谱 zeta 函数
DOI：
10.1007/s13226-015-0151-6
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
K. Furutani and C. Iwasaki
中科院分区：
文献类型：
--
作者：
W. Bauer;K. Furutani and C. Iwasaki
本文在Beals，Gaveau和Greiner的工作基础上，给出了两步幂零李群G上次拉普拉斯算子热核的显式积分形式.利用这样的积分形式，我们研究了nilmanifoldsL\G上的次拉普拉斯算子的热迹，其中L是一个格。作为一个应用，观察到了L\G上的次拉普拉斯的谱zeta函数的一个共同性质。特别是，我们引入了一类特殊的幂零李群，称为伪H型群，这是以前考虑的卡普兰群的推广。众所周知，这样的群总是允许格。在这里我们的目的是明确地计算各种低维紧致nilmanifoldsL\G上的（次）-Laplacian的热迹和谱，其中包括几个pseudoH-型nilmanifoldsL\G，即其中G是一个pseudoH-型群。在附录中，我们讨论了zeta函数，它通常表现为这些热迹的梅林变换。
We explain the explicit integral form of the heat kernel for the sub-Laplacian on two step nilpotent Lie groupsGbased on the work of Beals, Gaveau and Greiner. Using such an integral form we study the heat trace of the sub-Laplacian on nilmanifoldsL\GwhereLis a lattice. As an application a common property of the spectral zeta function for the sub-Laplacian onL\Gis observed. In particular, we introduce a special class of nilpotent Lie groups, called pseudoH-type groups which are generalizations of groups previously considered by Kaplan. As is known such groups always admit lattices. Here we aim to explicitly calculate the heat trace and the spectrum of the (sub)-Laplacian on various low dimensional compact nilmanifolds including several pseudoH-type nilmanifoldsL\G, i.e. whereGis a pseudoH-type group. In an appendix we discuss a zeta function which typically appears as the Mellin transform for these heat traces.