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Computer Physics Communications, ISSN 0010-4655, 01/2020, p. 107165
Journal Article
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 03/2019, Volume 2019, Issue 748, pp. 1 - 138
Hodge correlators are complex numbers given by certain integrals assigned to a smooth complex curve. We show that they are correlators of a Feynman integral,... 
POLYLOGARITHMS | MATHEMATICS | REGULATORS | GEOMETRY
Journal Article
Nagoya Mathematical Journal, ISSN 0027-7630, 12/2018, Volume 232, pp. 19 - 54
We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at nonpositive integers and whose values at positive integers... 
POLYLOGARITHMS | MATHEMATICS | VALUES | Integers
Journal Article
Nuclear and Particle Physics Proceedings, ISSN 2405-6014, 04/2016, Volume 273-275, pp. 2128 - 2135
In this contribution we review the status of higher-order QCD computations, focussing on recent progress in next-to-next-to-leading order and beyond. After a... 
QCD | polylogarithms | NNNLO | NNLO | Polylogarithms
Journal Article
Journal of Number Theory, ISSN 0022-314X, 08/2019, Volume 201, pp. 190 - 205
In this paper, we introduce modified finite polylogarithms, which are linear maps from the free abelian group generated by Q∖{0,1} to an adelic ring A. Then,... 
Mixed Tate motive | Finite polylogarithm | Étale polylogarithm
Journal Article
JOURNAL OF HIGH ENERGY PHYSICS, ISSN 1029-8479, 12/2013, Issue 12
We compute the contributions to the (NLO)-L-3 inclusive Higgs boson cross-section from the square of one-loop amplitudes with a Higgs boson and three QCD... 
NLO Computations | HADRON COLLIDERS | ASYMPTOTIC-EXPANSION | DIFFERENTIAL-EQUATIONS | PROTON COLLIDERS | NUMERICAL EVALUATION | BOSON PRODUCTION | FEYNMAN-INTEGRALS | MULTIPLE POLYLOGARITHMS | QCD Phenomenology | QCD CORRECTIONS | HARMONIC POLYLOGARITHMS | PHYSICS, PARTICLES & FIELDS
Journal Article
Journal of Number Theory, ISSN 0022-314X, 08/2018, Volume 189, pp. 25 - 80
This paper investigates the relations between modular graph forms, which are generalizations of the modular graph functions that were introduced in earlier... 
Eisenstein series | Duality | Modular forms | Superstrings | Modular graph functions | Polylogarithms | MATHEMATICS | VALUED MULTIPLE POLYLOGARITHMS
Journal Article
Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 2016, Volume 46, Issue 3, pp. 925 - 938
In 1887, beneath a canopy of stars, Srinivasa Ramanujan commenced his brief existence on this planet. In a universe at the mercy of its entropy, against all... 
Ramanujan | Polylogarithms | MATHEMATICS | polylogarithms
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 11/2014, Volume 47, Issue 47, p. 474005
Motivated by the cluster structure of two-loop scattering amplitudes in N = 4 Yang-Mills theory we define cluster polylogarithm functions. We find that all... 
Polylogarithms | Cluster algebras | Scattering amplitudes | scattering amplitudes | cluster algebras | PHYSICS, MULTIDISCIPLINARY | polylogarithms | PHYSICS, MATHEMATICAL
Journal Article
Turkish Journal of Mathematics, ISSN 1300-0098, 2018, Volume 42, Issue 3, pp. 1509 - 1527
In this article, a generalized geometry of Goncharov's complex and the Grassmannian complex will be proposed. First, all new homomorphisms will be defined, and... 
Grassmannian | Chain complexes | Generalization | Classical polylogarithms | POLYLOGARITHMS | MATHEMATICS | NUMBERS | chain complexes | generalization
Journal Article
JOURNAL OF PURE AND APPLIED ALGEBRA, ISSN 0022-4049, 07/2016, Volume 220, Issue 7, pp. 2590 - 2647
In this paper, we construct a family of algebraic cycles in Bloch's cycle complex over P-1 minus three points, which are expected to correspond to multiple... 
POLYLOGARITHMS | MATHEMATICS | MATHEMATICS, APPLIED | Algebra
Journal Article
JOURNAL OF NUMBER THEORY, ISSN 0022-314X, 08/2019, Volume 201, pp. 190 - 205
In this paper, we introduce modified finite polylogarithms, which are linear maps from the free abelian group generated by Q \ {0, 1} to an adelic ring A.... 
Etale polylogarithm | MATHEMATICS | FUNCTIONAL-EQUATIONS | Finite polylogarithm | Mixed Tate motive
Journal Article
Computer Physics Communications, ISSN 0010-4655, 07/2019, Volume 240, pp. 189 - 201
We present the FORTRAN-code HPOLY.f for the numerical calculation of harmonic polylogarithms up to w = 8 at an absolute accuracy of ∼10−15 or better. Using... 
Harmonic polylogarithms | Numeric representation | Cyclotomic harmonic polylogarithms | INTEGRALS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ANALYTIC CONTINUATION | MELLIN TRANSFORMS | PHYSICS, MATHEMATICAL | SUMS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 10/2015, Volume 268, pp. 462 - 477
This paper extends tools developed by Crandall (2012) [16] to provide robust, high-precision methods for computation of the incomplete Gamma function and the... 
Lerch transcendent function | Incomplete gamma function | Dirichlet L-series | Character polylogarithms | Polylogarithms | Hurwitz zeta function
Journal Article
Journal of Number Theory, ISSN 0022-314X, 07/2017, Volume 176, pp. 279 - 301
We show an explicit formula relating étale polylogarithms introduced by Wojtkowiak and finite polylogarithms introduced by Elbaz-Vincent and Gangl. This... 
Finite polylogarithm | Étale polylogarithm | Etale polylogarithm | MATHEMATICS | FUNCTIONAL-EQUATIONS | ADIC ITERATED INTEGRALS | ANALOG
Journal Article
PHYSICS LETTERS B, ISSN 0370-2693, 02/2018, Volume 777, pp. 394 - 398
We consider a planar double box with four massive external momenta and two massive internal propagators. We derive the system of differential equations for the... 
Massive Feynman integrals | TOPOLOGIES | FIESTA | IMPLEMENTATION | DIFFERENTIAL-EQUATIONS | PHYSICS, NUCLEAR | Scattering amplitudes | Canonical form | MULTIPLE POLYLOGARITHMS | FEYNMAN-INTEGRALS | ASTRONOMY & ASTROPHYSICS | 2-LOOP MASTER INTEGRALS | HARMONIC POLYLOGARITHMS | DIAGRAM | BHABHA SCATTERING | PHYSICS, PARTICLES & FIELDS
Journal Article
Nuclear Physics, Section B, ISSN 0550-3213, 06/2016, Volume 907, pp. 400 - 444
It is shown that the study of the imaginary part and of the corresponding dispersion relations of Feynman graph amplitudes within the differential equations... 
GRAPH | POLYLOGARITHMS | IDENTITIES | MASTER INTEGRALS | DIAGRAM | PHYSICS, PARTICLES & FIELDS | Differential equations | Physics - High Energy Physics - Phenomenology | Nuclear and High Energy Physics | High Energy Physics - Phenomenology | Physics
Journal Article
Annual Review of Nuclear and Particle Science, ISSN 0163-8998, 10/2019, Volume 69, Issue 1, pp. 15 - 39
Precise predictions for collider observables require the computation of higher orders in perturbation theory. This task usually involves the evaluation of... 
Feynman integrals | elliptic polylogarithms | multiple polylogarithms | Hopf algebras | GRAPH | YANG-MILLS | 4-POINT FUNCTIONS | DIFFERENTIAL-EQUATIONS | PHYSICS, NUCLEAR | ALGORITHMS | MODULI SPACES | ITERATED INTEGRALS | AMPLITUDES | OPERATORS | PHYSICS, PARTICLES & FIELDS
Journal Article
JOURNAL OF HIGH ENERGY PHYSICS, ISSN 1029-8479, 05/2018, Issue 5
We present the Higgs boson production cross section at Hadron colliders in the gluon fusion production mode through (NLO)-L-3 in perturbative QCD.... 
POLYLOGARITHMS | FEYNMAN-INTEGRALS | BETA-FUNCTION | Perturbative QCD | MASS | NNLO | 3-LOOP SPLITTING FUNCTIONS | DIFFERENTIAL-EQUATIONS | Higgs Physics | DIAGRAM | RENORMALIZATION | PHYSICS, PARTICLES & FIELDS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 10/2015, Volume 268, pp. 462 - 477
This paper extends tools developed by Crandall (2012) [16] to provide robust, high-precision methods for computation of the incomplete Gamma function and the... 
Lerch transcendent function | Incomplete gamma function | Dirichlet L-series | Character polylogarithms | Polylogarithms | Hurwitz zeta function | Poly logarithms | MATHEMATICS, APPLIED
Journal Article
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