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On a Class of Feynman Integrals Evaluating to Iterated Integrals of Modular Forms

  • Luise Adams
  • Stefan WeinzierlEmail author
Chapter
Part of the Texts & Monographs in Symbolic Computation book series (TEXTSMONOGR)

Abstract

In this talk we discuss a class of Feynman integrals, which can be expressed to all orders in the dimensional regularisation parameter as iterated integrals of modular forms. We review the mathematical prerequisites related to elliptic curves and modular forms. Feynman integrals, which evaluate to iterated integrals of modular forms go beyond the class of multiple polylogarithms. Nevertheless, we may bring for all examples considered the associated system of differential equations by a non-algebraic transformation to an \(\varepsilon \)-form, which makes a solution in terms of iterated integrals immediate.

Notes

Acknowledgements

S.W. would like to thank the organisers and KMPB for the organisation of the inspiring conference.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.PRISMA Cluster of Excellence, Institut für PhysikJohannes Gutenberg-Universität MainzMainzGermany

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