Journal of number theory, ISSN 0022-314X, 2018, Volume 189, pp. 25 - 80

... energy expansion of genus-one Type II superstring amplitudes. These modular graph forms are multiple sums associated with decorated Feynman graphs on the world-sheet torus...

Eisenstein series | Duality | Modular forms | Superstrings | Modular graph functions | Polylogarithms | MATHEMATICS | VALUED MULTIPLE POLYLOGARITHMS

Eisenstein series | Duality | Modular forms | Superstrings | Modular graph functions | Polylogarithms | MATHEMATICS | VALUED MULTIPLE POLYLOGARITHMS

Journal Article

Communications in number theory and physics, ISSN 1931-4523, 2017, Volume 11, Issue 1, pp. 165 - 218

.... We here introduce a class of single-valued elliptic multiple polylogarithms, which are defined as elliptic functions associated with Feynman graphs with vanishing external momenta at all but two vertices...

INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | TRANSCENDENTAL FUNCTIONS | PERIODS | SPACES | EXPANSION | VALUED MULTIPLE POLYLOGARITHMS | ZETA VALUES | AMPLITUDES | PHYSICS, MATHEMATICAL

INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | TRANSCENDENTAL FUNCTIONS | PERIODS | SPACES | EXPANSION | VALUED MULTIPLE POLYLOGARITHMS | ZETA VALUES | AMPLITUDES | PHYSICS, MATHEMATICAL

Journal Article

Journal of number theory, ISSN 0022-314X, 2015, Volume 148, pp. 478 - 506

.... In this paper we prove this conjecture by constructing a certain family of single-valued multiple polylogarithms which correspond to multiple zeta values ζ(2,…,2,3,2,…2...

Multiple zeta values | Quantum field theory | Single-valued polylogarithms | DIAGRAMS | MATHEMATICS | DIMENSIONS | NUMBERS | ALGEBRA | LOOPS | MOTIVES

Multiple zeta values | Quantum field theory | Single-valued polylogarithms | DIAGRAMS | MATHEMATICS | DIMENSIONS | NUMBERS | ALGEBRA | LOOPS | MOTIVES

Journal Article

Physical review. D, ISSN 2470-0029, 2018, Volume 97, Issue 8

We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. These results are the...

INTEGRALS | PERIODS | ASTRONOMY & ASTROPHYSICS | VALUED MULTIPLE POLYLOGARITHMS | GRAPHICAL FUNCTIONS | ELECTRON G-2 | C INVARIANTS | MASSLESS PROPAGATORS | MOTIVES | COACTION | PHYSICS, PARTICLES & FIELDS | Mathematical Physics | High Energy Physics - Theory | Mathematics - Number Theory

INTEGRALS | PERIODS | ASTRONOMY & ASTROPHYSICS | VALUED MULTIPLE POLYLOGARITHMS | GRAPHICAL FUNCTIONS | ELECTRON G-2 | C INVARIANTS | MASSLESS PROPAGATORS | MOTIVES | COACTION | PHYSICS, PARTICLES & FIELDS | Mathematical Physics | High Energy Physics - Theory | Mathematics - Number Theory

Journal Article

COMMUNICATIONS IN NUMBER THEORY AND PHYSICS, ISSN 1931-4523, 2017, Volume 11, Issue 3, pp. 657 - 705

We report on calculations of Feynman periods of primitive log-divergent phi(4) graphs up to eleven loops. The structure of phi(4) periods is described by a...

MATHEMATICS, APPLIED | THEOREM | VALUED MULTIPLE POLYLOGARITHMS | QUANTUM-FIELD THEORY | PHYSICS, MATHEMATICAL | CONJECTURE | DIAGRAMS | MATHEMATICS | FEYNMAN-INTEGRALS | GRAPH POLYNOMIALS | ZETA VALUES | LOOPS | MOTIVES

MATHEMATICS, APPLIED | THEOREM | VALUED MULTIPLE POLYLOGARITHMS | QUANTUM-FIELD THEORY | PHYSICS, MATHEMATICAL | CONJECTURE | DIAGRAMS | MATHEMATICS | FEYNMAN-INTEGRALS | GRAPH POLYNOMIALS | ZETA VALUES | LOOPS | MOTIVES

Journal Article

Letters in mathematical physics, ISSN 0377-9017, 06/2017, Volume 107, Issue 6, pp. 1177 - 1192

Graphical functions are positive functions on the punctured complex plane which arise in quantum field theory. We generalize a parametric integral...

Feynman integrals | Perturbation theory | Graphical functions | Parametric representation | POLYNOMIALS | FEYNMAN-INTEGRALS | THEOREM | VALUED MULTIPLE POLYLOGARITHMS | PROOF | PHYSICS, MATHEMATICAL

Feynman integrals | Perturbation theory | Graphical functions | Parametric representation | POLYNOMIALS | FEYNMAN-INTEGRALS | THEOREM | VALUED MULTIPLE POLYLOGARITHMS | PROOF | PHYSICS, MATHEMATICAL

Journal Article

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