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

2019 ◽  
pp. 29-49 ◽  
Author(s):  
Luise Adams ◽  
Stefan Weinzierl
Keyword(s):  
Modular Forms ◽  
Iterated Integrals ◽  
Feynman Integrals

scholarly journals Three-loop contributions to the ρ parameter and iterated integrals of modular forms

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Samuel Abreu ◽  
Matteo Becchetti ◽  
Claude Duhr ◽  
Robin Marzucca
Keyword(s):  
Modular Forms ◽  
Iterated Integrals

scholarly journals Gross–Stark units and p-adic iterated integrals attached to modular forms of weight one

2016 ◽  
Vol 40 (2) ◽  
pp. 325-354 ◽  
Author(s):  
Henri Darmon ◽  
Alan Lauder ◽  
Victor Rotger
Keyword(s):  
Modular Forms ◽  
Iterated Integrals ◽  
Weight One ◽  
Stark Units

scholarly journals Period functions associated to real-analytic modular forms

2020 ◽  
Vol 7 (3) ◽  
Author(s):  
Nikolaos Diamantis ◽  
Joshua Drewitt
Keyword(s):  
Modular Forms ◽  
Special Interest ◽  
Iterated Integrals ◽  
Real Analytic ◽  
Period Polynomial

Abstract We define L-functions for the class of real-analytic modular forms recently introduced by F. Brown. We establish their main properties and construct the analogue of period polynomial in cases of special interest, including those of modular iterated integrals of length one.

scholarly journals Modular iterated integrals associated with cusp forms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolaos Diamantis
Keyword(s):  
Modular Forms ◽  
Higher Order ◽  
New Method ◽  
Independent Interest ◽  
Cusp Forms ◽  
Fuchsian Groups ◽  
Modular Invariant ◽  
Iterated Integrals ◽  
Invariant Functions

Abstract We construct an explicit family of modular iterated integrals which involves cusp forms. This leads to a new method of producing modular invariant functions based on iterated integrals of modular forms. The construction will be based on an extension of higher-order modular forms which, in contrast to the standard higher-order forms, applies to general Fuchsian groups of the first kind and, as such, is of independent interest.

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