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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Pierre Lairez. Computing periods of rational integrals. Mathematics of Computation, American Mathematical Society, 2016, 85, pp.1719-1752. ⟨http://www.ams.org/journals/mcom/2016-85-300/S0025-5718-2015-03054-3/⟩. ⟨10.1090/mcom/3054⟩. ⟨hal-00981114v3⟩

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