Periods and Igusa Zeta functions

TL;DR

This paper proves that coefficients of Igusa Zeta functions' Laurent series are periods, linking number theory with algebraic geometry and setting the stage for applications in Feynman amplitude analysis.

Contribution

It establishes that Laurent series coefficients of Igusa Zeta functions are periods, a novel connection in the study of these functions.

Findings

Coefficients in Laurent series are periods

Foundation for showing Feynman amplitude numbers are periods

Links number theory with algebraic geometry

Abstract

We show that coefficients in the Laurent series of Igusa Zeta functions are periods. This will be used in a subsequent paper (by P. Brosnan) to show that certain numbers occurring in study of Feynman amplitudes (upto gamma factors) are periods.