Selberg's trace formula as applied to a compact riemann surface
Selberg's trace formula as applied to a compact riemann surface
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应用于紧致黎曼曲面的塞尔伯格迹公式
DOI：
10.1002/cpa.3160250302
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发表时间：
1972
影响因子：
3
通讯作者：
H. McKean
中科院分区：
文献类型：
--
作者：
H. McKean
The purpose of this paper is to explain the application of the trace formula ofA. Selberg [1 13 to compact Riemann surfaces with two or more handles. For surfaces with one handle (tori), the role of Selberg’s formula is played by the classical Poisson summation formula; in fact, Selberg’s formula may be thought of as non-commutative analogue of the latter. From the standpoint of complex function theory, a torus M- is the plane factored by an integral lattice L with “periods” 1 and a+ J-1 b, b> 0. The eigenfunctions of the Laplacian A= 8/ax:+ 8/ax: on M are the exponentials exp (27rJ-1 w’* x} with periods from L, or what is the same, with wave numbers from the dual lattice L’of points w ‘for which w ‘* w is integral for every period o from L. The corresponding eigenvalues are-4r2 lo’(2, and the Poisson summation formula relates the “theta” function for the dual lattice
