Spectrum of a compact flat manifold
Spectrum of a compact flat manifold
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紧凑型扁平歧管的频谱
DOI：
10.1007/bf02566102
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发表时间：
1978
期刊：
影响因子：
--
通讯作者：
T. Sunada
中科院分区：
文献类型：
--
作者：
T. Sunada
从微分几何的观点出发，给出了R”中L格上Dirichlet级数的著名Jacobi恒等式：exp（-hit）= λ（L\R”）（4 zrt）-"/2~ exp（-l（cx）2/4 t）i= Ox ~ L（t> 0），其中级数0= Ao<A1 ~ A2~. c~是平坦环面L\R”上的Laplacian ~= 1（0/Oxi）2的谱，l（cx）表示L\R”中属于同伦类x的闭测地线cx的长度.这里我们将L与基本群~ rl（L\R”）等同起来。
From the differential geometric view point, the celebrated Jacobi identity for a Dirichlet series associated with a lattice L in R" is written as exp (-hit)= Vol (L\R")(4zrt)-"/2~ exp (-l (cx) 2/4t) i= O x~ L (t> O), in which the series 0= Ao< A 1~ A2~....~ c~ is the spectrum of the Laplacian-~= 1 (0/Oxi) 2 on a flat torus L\R", and l (cx) stands for the length of a closed geodesic cx in L\R" belonging to the homotopy class x. Here we identify L with the fundamental group~ rl (L\R").