论文标题
一般重排的引理，用于非共同托里的热痕量渐近线
General Rearrangement Lemma for Heat Trace Asymptotic on Noncommutative Tori
论文作者
论文摘要
我们研究了由非交通性托里的光谱几何形状引起的技术问题：与一般二阶椭圆算子相关的小时热量痕量渐近线。我们使用格拉曼尼亚人的超几何积分将保形案例中的重排算子扩展到一般环境。主要的结果是第二热系数的明确公式就系数而言。当专门研究共形案例中的示例时，我们不仅在以前的工作中恢复结果，而且还获得了一些额外的功能关系，这些功能关系为主要结果提供了实验支持。最后，我们基于从超几何特征得出的组合特性来验证关系。
We study a technical problem arising from the spectral geometry of noncommutative tori: the small time heat trace asymptotic associated to a general second order elliptic operator. We extend the rearrangement operators in the conformal case to the general setting using hypergeometric integrals over Grassmannians. The main result is the explicit formula of the second heat coefficient in terms of the coefficients. When specializing to examples in conformal case, we not only recover results in previous works but also obtain some extra functional relations whose validation provides experimental support to the main results. At last, we verify the relations based on combinatorial properties derived from the hypergeometric features.
