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In these proceedings we discuss a representation for modular forms that is more suitable for their application to the calculation of Feynman integrals in the context of iterated integrals and the differential equation method.
Differential equations method: New technique for massive Feynman diagrams calculation
A. V. Kotikov · 1991
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Differential equations for Feynman graph amplitudes
Ettore Remiddi · 1997
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Differential equations for two loop four point functions
T. Gehrmann and E. Remiddi · 2000
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Analytic treatment of the two loop equal mass sunrise graph
S. Laporta and E. Remiddi · 2005
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On Rationally Parametrized Modular Equations
R. S. Maier · 2006
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Elliptic Modular Forms and Their Applications
Don Zagier · 2008
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Multiple Elliptic Polylogarithms
Francis Brown and Andrey Levin · 2011
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Modular polynomials via isogeny volcanoes
Reinier Broker, Kristin Lauter, and Andrew V. Sutherland · 2012
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Multiloop integrals in dimensional regularization made simple
Johannes M. Henn · 2013
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Multiple Modular Values and the relative completion of the fundamental group of M 1 , 1 M_{1,1}
Francis Brown · 2014
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The elliptic dilogarithm for the sunset graph
Spencer Bloch and Pierre Vanhove · 2015
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Elliptic multiple zeta values and one-loop superstring amplitudes
Johannes Broedel, Carlos R. Mafra, Nils Matthes, and Oliver Schlotterer · 2015
Cited alongside, same era.
Two-loop planar master integrals for Higgs → 3 \to 3 partons with full heavy-quark mass dependence
Roberto Bonciani, Vittorio Del Duca, Hjalte Frellesvig, Johannes M. Henn, Francesco Moriello, and Vladimir A. Smirnov · 2016
Cited alongside, same era.
Relations between elliptic multiple zeta values and a special derivation algebra
Johannes Broedel, Nils Matthes, and Oliver Schlotterer · 2016
Cited alongside, same era.
Class polynomials for nonholomorphic modular functions
Jan Hendrik Bruinier, Ken Ono, and Andrew V. Sutherland · 2016
Cited alongside, same era.
Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral
Ettore Remiddi and Lorenzo Tancredi · 2016
Cited alongside, same era.
Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph
Amedeo Primo and Lorenzo Tancredi · 2017
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On the maximal cut of Feynman integrals and the solution of their differential equations
Amedeo Primo and Lorenzo Tancredi · 2017
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An Elliptic Generalization of Multiple Polylogarithms
Ettore Remiddi and Lorenzo Tancredi · 2017
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A non-planar two-loop three-point function beyond multiple polylogarithms
Andreas von Manteuffel and Lorenzo Tancredi · 2017
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Analytic results for the planar double box integral relevant to top-pair production with a closed top loop
Luise Adams, Ekta Chaubey, and Stefan Weinzierl · 2018
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Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations
J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, E. Imamoglu, M. van Hoeij, A. von Manteuffel, C. G. Raab, C. S. Radu, and C. Schneider · 2017
Cited alongside, same era.
Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
J. Ablinger, J. Blümlein, A. De Freitas, M. van Hoeij, E. Imamoglu, C. G. Raab, C. S. Radu, and C. Schneider · 2017
Cited alongside, same era.
Feynman integrals and iterated integrals of modular forms
Luise Adams and Stefan Weinzierl · 2017
Cited alongside, same era.
Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism
Johannes Broedel, Claude Duhr, Falko Dulat, and Lorenzo Tancredi · 2017
Cited alongside, same era.
Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral
Johannes Broedel, Claude Duhr, Falko Dulat, and Lorenzo Tancredi · 2017
Cited alongside, same era.
http://www.sagemath.org/
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https://math.mit.edu/~drew/classicalmodpolys.html
Cited in the paper.
The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter
Luise Adams, Ekta Chaubey, and Stefan Weinzierl · 2018
Closest in time.
The ε \varepsilon -form of the differential equations for Feynman integrals in the elliptic case
Luise Adams and Stefan Weinzierl · 2018
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Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series
Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, and Lorenzo Tancredi · 2018
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Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes
Johannes Broedel, Nils Matthes, Gregor Richter, and Oliver Schlotterer · 2018
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From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
Johannes Broedel, Oliver Schlotterer, and Federico Zerbini · 2018
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