AI 中文总结
研究具有有限维酉表示扭曲的双曲轨形面的塞尔伯格zeta函数，通过拉普拉斯共振等建立因式分解公式，推广前人结果，解释其零点和极点，轨形奇点在未扭曲时也对公式有新贡献。
AI 中文摘要
对于具有有限维酉表示扭曲的几何有限无限面积双曲轨形面的塞尔伯格zeta函数，我们根据所考虑双曲轨形面的拉普拉斯共振的魏尔斯特拉斯乘积、巴恩斯G函数、伽马函数和表示的奇点度数建立了一个因式分解公式。由此，我们通过轨形面和表示的谱和几何实体对塞尔伯格zeta函数的零点和极点进行了解释。该公式将博思威克、贾奇和佩里的因式分解结果推广到具有轨形奇点的双曲轨形面以及酉扭曲情况。在未扭曲的情况下，轨形奇点的存在也对因式分解公式产生了一个单独的、以前未观察到的贡献。
英文摘要
For the Selberg zeta function of geometrically finite infinite-area hyperbolic orbisurfaces with twists by finite-dimensional unitary representations, we establish a factorization formula in terms of a Weierstrass product of the Laplace resonances of the considered hyperbolic orbisurface, Barnes G-functions, gamma functions, and the singularity degrees of the representation. We thereby provide an interpretation of the zeros and poles of the Selberg zeta function by spectral and geometric entities of the orbisurface and the representation. This formula generalizes the factorization result by Borthwick, Judge and Perry to hyperbolic orbisurfaces with orbifold singularities as well as to unitary twists. Also in the untwisted case, the presence of orbifold singularities yields a separate, previously unobserved contribution to the factorization formula.
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