Periods and Igusa local zeta functions

@inproceedings{Belkale2003PeriodsAI,
  title={Periods and Igusa local zeta functions},
  author={Prakash Belkale and Patrick Brosnan},
  year={2003}
}
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. 

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