Spectral functions, special functions and the Selberg zeta function
Spectral functions, special functions and the Selberg zeta function
复制标题
DOI：
10.1007/bf01212422
复制
发表时间：
1987-09
影响因子：
2.4
通讯作者：
A. Voros
中科院分区：
文献类型：
--
作者：
A. Voros
由Zeta正则化定义的特征值序列的函数行列式可以简单地用求积法来计算。我们将这一过程应用于紧Riemann曲面的Selberg迹公式，得到Selberg Zeta函数的因式分解为两个函数行列式，分别与紧曲面本身和球面上的拉普拉斯函数有关。我们还将我们的形式应用于各种显本征值序列，以更简单的方式重现了关于Gamma函数和BarensG-函数的经典结果。对于后者，我们的方法解释了它与Selberg Zeta函数的联系，并计算了相关的Glaisher-Kinkelin Constanta。
The functional determinant of an eigenvalue sequence, as defined by zeta regularization, can be simply evaluated by quadratures. We apply this procedure to the Selberg trace formula for a compact Riemann surface to find a factorization of the Selberg zeta function into two functional determinants, respectively related to the Laplacian on the compact surface itself, and on the sphere. We also apply our formalism to various explicit eigenvalue sequences, reproducing in a simpler way classical results about the gamma function and the BarnesG-function. Concerning the latter, our method explains its connection to the Selberg zeta function and evaluates the related Glaisher-Kinkelin constantA.