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Computing periods of rational integrals


Author: Pierre Lairez
Journal: Math. Comp. 85 (2016), 1719-1752
MSC (2010): Primary 68W30; Secondary 14K20, 14F40, 33F10
DOI: https://doi.org/10.1090/mcom/3054
Published electronically: November 6, 2015
MathSciNet review: 3471105
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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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Additional Information

Pierre Lairez
Affiliation: Inria Saclay, équipe Specfun, France
Address at time of publication: Fäki;tat II, Sekr. 3-2, Technische Universität zu Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
Email: pierre@lairez.fr

DOI: https://doi.org/10.1090/mcom/3054
Keywords: Integration, periods, Picard-Fuchs equation, Griffiths-Dwork reduction, algorithms
Received by editor(s): May 6, 2014
Received by editor(s) in revised form: January 31, 2015
Published electronically: November 6, 2015
Article copyright: © Copyright 2015 American Mathematical Society