论文标题
威尔阳性和痕量配方，阿基米德岛
Weil positivity and Trace formula, the archimedean place
论文作者
论文摘要
我们使用本文“非共同几何形状中的痕迹公式和riemann zeta函数的零”的半局部痕量公式的希尔伯特空间框架提供了Weil功能的阳性的潜在概念原因。 （SelectaMath。5（1999），第1、29--106号）。我们详细探讨了单个Archimedean Place的最简单情况。 The root of the positivity is the trace of the scaling action compressed onto the orthogonal complement of the range of the cutoff projections associated to the cutoff in phase space, for cutoff parameter equal to 1. We express the difference between the Weil distribution and the Sonin trace (coming from the above compression of the scaling action) in terms of prolate spheroidal wave functions, and use as a key device the theory of hermitian Toeplitz matrices to control the difference.在一般的半局部情况下，上面使用的所有成分和工具都是有意义的，其中Weil阳性意味着RH。
We provide a potential conceptual reason for the positivity of the Weil functional using the Hilbert space framework of the semi-local trace formula of the paper "Trace formula in noncommutative geometry and the zeros of the Riemann zeta function". (Selecta Math. 5 (1999), no. 1, 29--106). We explore in great details the simplest case of the single archimedean place. The root of the positivity is the trace of the scaling action compressed onto the orthogonal complement of the range of the cutoff projections associated to the cutoff in phase space, for cutoff parameter equal to 1. We express the difference between the Weil distribution and the Sonin trace (coming from the above compression of the scaling action) in terms of prolate spheroidal wave functions, and use as a key device the theory of hermitian Toeplitz matrices to control the difference. All the ingredients and tools used above make sense in the general semi-local case, where Weil positivity implies RH.
