Periods and Igusa local zeta functions
Periods and Igusa local zeta functions
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周期和 Igusa 局部 zeta 函数
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
P. Brosnan
中科院分区：
文献类型：
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作者：
P. Belkale;P. Brosnan
我们证明了Igusa局部zeta函数I（s）=<$Cf ω的Laurent级数中的系数是周期的.这是证明了第一次显示这些功能的功能方程的存在。这将被用来在随后的论文（由P. Brosnan）中表明，费曼振幅中出现的某些数字（直到伽马因子）是周期。给出了主要结果的几个例子，其中一个例子表明欧拉常数γ是指数周期的.
We show that the coefficients in the Laurent series of the Igusa local zeta functions I(s) = ∫ C fω are periods. This is proved by first showing the existence of functional equations for these functions. This will be used to show in a subsequent paper (by P. Brosnan) that certain numbers occurring in Feynman amplitudes (up to Gamma factors) are periods. We also give several examples of our main result, and one example showing that Euler’s constant γ is an exponential period.