AI 中文总结
本文计算orbifold与等变挠的正线丛p次幂全纯挠渐近展开的log p部分，基于此推导Arakelov几何中的等变算术Hilbert-Samuel定理。
AI 中文摘要
我们利用示性类计算正线丛p次幂的全纯挠渐近展开的log p部分，该计算针对orbifold挠与等变挠完成；等变情形下，展开中的指数不超过不动点集的维数，我们由此推导出Arakelov几何中对应的等变算术Hilbert-Samuel定理。
英文摘要
We compute the $\log p$-part of the asymptotic expansion of the holomorphic torsion of the $p$-th power of a positive line bundle in terms of characteristic classes. This is done for orbifold and equivariant torsions. In the equivariant case the exponents in the expansion are less than or equal to the dimension of the fixed point set. We deduce a corresponding equivariant arithmetic Hilbert-Samuel theorem in Arakelov geometry.
