Fourier series of modular graph functions

Fourier series of modular graph functions - ScienceDirect

Modular graph functions associate to a graph an S L ( 2 , Z ) -invariant function on the upper half plane. We obtain the Fourier series of modular graph ...

[1708.07998] Fourier series of modular graph functions - arXiv

We obtain the Fourier series of modular graph functions of arbitrary weight w and two-loop order. The motivation for this work is to develop a deeper ...

Fourier series of modular graph functions - UCLA Mathematics

Abstract. Modular graph functions associate to a graph an SL(2,Z)-invariant function on the upper half plane. We obtain the Fourier series ...

(PDF) Fourier series of modular graph functions - ResearchGate

Modular graph functions associate to a graph an $SL(2,Z)$-invariant function on the upper half plane. We obtain the Fourier series of ...

Fourier series of modular graph functions - Inspire HEP

Fourier series of modular graph functions. Eric D'Hoker(. UCLA. ) ,. William Duke(. UCLA, Math. Dept. ) Aug 26, 2017. 36 pages. Published in: J.Number Theor ...

Fourier series of modular graph functions - Scite

“…In the present paper, we shall obtain the Fourier series, including constant and nonconstant Fourier modes, of arbitrary two-loop modular graph functions, ...

Notes on Fourier Series and Modular Forms - Brown Math Department

Our results about Fourier series are proved for functions that have somewhat artificial restrictions placed on them. We do this so as to avoid any nontrivial ...

Zero mode of the Fourier series of some modular graphs from ...

We consider specific linear combinations of two loop modular graph functions on the toroidal worldsheet with 2s links for s = 2 , 3 and 4.

Zero mode of the Fourier series of some modular graphs from ... - arXiv

We consider modular graph functions [1,2] that arise in the low momentum expansion of multi–graviton amplitudes in type II string theory at ...

Modular graph functions and odd cuspidal functions. Fourier and ...

For one-loop graphs they reduce to real analytic Eisenstein series. We obtain the Fourier series, including the constant and non-constant ...

Zero mode of the Fourier series of some modular ... - NASA ADS

Abstract. We consider specific linear combinations of two loop modular graph functions on the toroidal worldsheet with 2s links for s = 2 , 3 and 4.

Modular Graph Functions - HAL

The simplest case is C1,1,1 = E3 + ζ(3), which is manifestly compatible, in view of the Fourier mode expansion of the Eisenstein series given in ...

Fourier series of modular graph functions

Modular graph functions associate to a graph an SL(2,Z)-invariant function on the upper half plane. We obtain the Fourier series of modular graph functions ...

Fourier series of modular graph functions - OUCI

Basu, Poisson equation for the three loop ladder diagram in string theory at genus one, Internat. · Basu, Proving relations between modular graph functions, ...

[PDF] Modular graph functions and odd cuspidal ... - Semantic Scholar

Eisenstein series. We obtain the Fourier series, including the constant and non-constant Fourier modes, of all two-loop modular graph functions, as well as ...

Modular graph functions - UCLA Physics & Astronomy

Hierarchy of Modular Graph Identities. • ED and W. Duke, JNT 192 (2018) 1-36, arXiv:1708.07998,. Fourier series of modular graph functions. • ED, M.B. Green, B ...

Modular graph functions

which is manifestly compatible, in view of the Fourier mode expansion of the Eisenstein series given in the preceding section. The cases of weight 4 and 5 ...

Plotting graphs of Modular Forms - Mathematics Stack Exchange

The first is this " .. To produce the plots, we approximate each modular form by its first 400 Fourier coefficients and evaluate the function on ...

Modular graph functions and odd cuspidal functions. Fourier and ...

Modular graph functions are SL(2, &Z;)-invariant functions associated with Feynman graphs of a two-dimensional conformal field theory on a torus of modulus ...

Modular Functions with Rational Fourier Expansions - MathOverflow

That is, after fixing a hauptmodul h with rational fourier expansion, so that any modular function for Γ0(N) can be written as a rational ...