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

We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalization of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. We study the properties of our iterated integrals and their relationship to the multiple elliptic polylogarithms from the mathematics literature. On the one hand, we find that our iterated integrals span essentially the same space of functions as the multiple elliptic polylogarithms. On the other, our formulation allows for a more direct use to solve a large variety of problems in high-energy physics. As a result, we demonstrate the use of our functions in the evaluation of the Laurent expansion of some hypergeometric functions for values of the indices close to half integers.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. Humboldt-Univ. zu Berlin, Berlin (Germany)
  2. European Organization for Nuclear Research (CERN), Geneva (Switzerland); Univ. Catholique de Louvain, Louvain-La-Neuve (Belgium)
  3. Stanford Univ., Stanford, CA (United States)
  4. European Organization for Nuclear Research (CERN), Geneva (Switzerland)
Publication Date:
Grant/Contract Number:
AC02-76SF00515
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 5; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; NLO Computations; QCD Phenomenology
OSTI Identifier:
1458523

Broedel, Johannes, Duhr, Claude, Dulat, Falko, and Tancredi, Lorenzo. Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism. United States: N. p., Web. doi:10.1007/jhep05(2018)093.
Broedel, Johannes, Duhr, Claude, Dulat, Falko, & Tancredi, Lorenzo. Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism. United States. doi:10.1007/jhep05(2018)093.
Broedel, Johannes, Duhr, Claude, Dulat, Falko, and Tancredi, Lorenzo. 2018. "Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism". United States. doi:10.1007/jhep05(2018)093. https://www.osti.gov/servlets/purl/1458523.
@article{osti_1458523,
title = {Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism},
author = {Broedel, Johannes and Duhr, Claude and Dulat, Falko and Tancredi, Lorenzo},
abstractNote = {We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalization of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. We study the properties of our iterated integrals and their relationship to the multiple elliptic polylogarithms from the mathematics literature. On the one hand, we find that our iterated integrals span essentially the same space of functions as the multiple elliptic polylogarithms. On the other, our formulation allows for a more direct use to solve a large variety of problems in high-energy physics. As a result, we demonstrate the use of our functions in the evaluation of the Laurent expansion of some hypergeometric functions for values of the indices close to half integers.},
doi = {10.1007/jhep05(2018)093},
journal = {Journal of High Energy Physics (Online)},
number = 5,
volume = 2018,
place = {United States},
year = {2018},
month = {5}
}