Vladimirov导数的Green函数与Tate命题
Green's Functions for Vladimirov Derivatives and Tate's Thesis
摘要：
给定一个具有Hecke特征标$χ$的数域$K$，对每一个位置$ν$，我们研究其动力学项由与$χ$的局部分量相关的正则化Vladimirov导数给出的自由标量场.这些理论出现在$p$ -adic弦论和$p$ -adic AdS/CFT对应的研究中。我们证明了正则化Vladimirov导数的$χ$的局部分量的傅立叶共轭的公式。我们发现格林函数由Zeta积分的局部泛函方程给出。此外，考虑到所有的位置$ν$，对应于格林函数的场论两点函数满足一个直积公式，这等价于Zeta积分的整体函数方程.特别是，这指出了一个作用泰特的论文在adelic物理学。
英文摘要：
Given a number field $K$ with a Hecke character $χ$, for each place $ν$ we study the free scalar field theory whose kinetic term is given by the regularized Vladimirov derivative associated to the local component of $χ$. These theories appear in the study of $p$-adic string theory and $p$-adic AdS/CFT correspondence. We prove a formula for the regularized Vladimirov derivative in terms of the Fourier conjugate of the local component of $χ$. We find that the Green's function is given by the local functional equation for Zeta integrals. Furthermore, considering all places $ν$, the field theory two-point functions corresponding to the Green's functions satisfy an adelic product formula, which is equivalent to the global functional equation for Zeta integrals. In particular, this points out a role of Tate's thesis in adelic physics.
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