Higher holonomy and iterated integrals

2021 ◽  
pp. 309-328
Author(s):  
Toshitake Kohno
Keyword(s):  
Iterated Integrals

scholarly journals Master integrals for bipartite cuts of three-loop photon self energy

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
R. N. Lee ◽  
A. I. Onishchenko
Keyword(s):  
Spectral Density ◽  
High Energy ◽  
Elliptic Integrals ◽  
Iterated Integrals ◽  
Self Energy ◽  
Complete Elliptic Integrals ◽  
The One

Abstract We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the 4m cut (the cut of 4 massive lines), reduce to Goncharov’s polylogarithms. The master integrals for 4m cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for 4m cut.

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 Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

2018 ◽  
Vol 2018 (5) ◽  
Author(s):  
Johannes Broedel ◽  
Claude Duhr ◽  
Falko Dulat ◽  
Lorenzo Tancredi
Keyword(s):  
Elliptic Curves ◽  
Iterated Integrals

scholarly journals On l-Adic Iterated Integrals, II Functional Equations and l-Adic Polylogarithms

2005 ◽  
Vol 177 ◽  
pp. 117-153 ◽  
Author(s):  
Zdzislaw Wojtkowiak
Keyword(s):  
Functional Equations ◽  
Iterated Integrals

We continue to study l-adic iterated integrals introduced in the first part. We shall show that the l-adic iterated integrals satisfy essentially the same functional equations as the classical complex iterated integrals. Next we are studying l-adic analogs of classical polylogarithms.

scholarly journals Hoffman’s conjectural identity

2019 ◽  
Vol 15 (01) ◽  
pp. 167-171 ◽  
Author(s):  
Minoru Hirose ◽  
Nobuo Sato
Keyword(s):  
Multiple Zeta Values ◽  
Iterated Integrals ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Special Case

In this paper, we prove a family of identities among multiple zeta values, which contains as a special case a conjectural identity of Hoffman. We use the iterated integrals on [Formula: see text] for our proof.

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