Computing periods of rational integrals

Pierre Lairez 1, *
* Corresponding author
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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https://hal.inria.fr/hal-00981114
Contributor : Pierre Lairez <>
Submitted on : Tuesday, May 6, 2014 - 11:17:39 AM
Last modification on : Wednesday, September 2, 2015 - 1:06:08 AM

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  • HAL Id : hal-00981114, version 2

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Pierre Lairez. Computing periods of rational integrals. 2014. ⟨hal-00981114v2⟩

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