论文标题
格林的弗拉基米罗夫衍生品和泰特论文的功能
Green's Functions for Vladimirov Derivatives and Tate's Thesis
论文作者
论文摘要
给定一个带有hecke字符$χ$的数字字段$ k $，对于每个位置$ν$，我们研究了自由标量场理论，其动力学术语由正规化的vladimirov衍生物给出，与$χ$的本地组件相关。这些理论出现在$ p $ - adiC string理论和$ p $ - adic Ads/CFT通信的研究中。我们证明了根据$χ$的本地组件的傅立叶结合物的正则化vladimirov衍生物的公式。我们发现绿色的函数由Zeta积分的局部功能方程式给出。此外，考虑到所有位置$ν$，与绿色功能相对应的字段理论两点函数满足了Adelic产品公式，该公式与Zeta积分的全局功能方程相当。特别是，这指出了泰特论文在Adelic Physics中的作用。
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.
