尖点流形上eta函数的正则性
Regularity of the eta function on manifolds with cusps
摘要：
在具有共形尖点的自旋流形上，证明了在无穷远处可逆条件下，扭Dirac算子的eta函数至多有单极点，且在原点正则.对于有限体积的双曲流形，证明了被任何齐次向量丛扭曲的Dirac算子的eta函数是整函数.
英文摘要：
On a spin manifold with conformal cusps, we prove under an invertibility condition at infinity that the eta function of the twisted Dirac operator has at most simple poles and is regular at the origin. For hyperbolic manifolds of finite volume, the eta function of the Dirac operator twisted by any homogeneous vector bundle is shown to be entire.
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