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arXiv · 1404.5069

Computing periods of rational integrals

Pierre Lairez
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Abstract

A period of a rational integral is the result of integrating, with respect to one or several variables, a rational function over a closed path. This work focuses particularly on periods depending on a parameter: in this case the period under consideration satisfies a linear differential equation, the Picard-Fuchs equation. I give a reduction algorithm that extends the Griffiths-Dwork reduction and apply it to the computation of Picard-Fuchs equations. The resulting algorithm is elementary and has been successfully applied to problems that were previously out of reach.

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Pierre Lairez. 2014-04-20. Computing periods of rational integrals. https://doi.org/10.1090/mcom/3054

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