论整体 D 模块的傅立叶变换的无穷大单色性

Kazuki Kudomi, Kiyoshi Takeuchi
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引用次数: 0

摘要

基于不规则黎曼-希尔伯特对应关系的最新进展,我们研究了在某些情况下整体性 D 模块的傅里叶变换全形解的无穷大处单色性。通过将单旋转zeta函数理论应用于我们之前关于傅里叶变换的增强解复数的结果,我们得到了特征值的公式。特别是,在维数一中,我们发现了整体 D 模块的无穷大处单色性与它们的傅里叶变换之间的互易律。
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On the monodromies at infinity of Fourier transforms of holonomic D-modules
Based on the recent progress in the irregular Riemann-Hilbert correspondence, we study the monodromies at infinity of the holomorphic solutions of Fourier transforms of holonomic D-modules in some situations. Formulas for their eigenvalues are obtained by applying the theory of monodromy zeta functions to our previous results on the enhanced solution complexes of the Fourier transforms. In particular, in dimension one we thus find a reciprocity law between the monodromies at infinity of holonomic D-modules and their Fourier transforms.
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