Fourier series of modular graph functions

DOI10.1016/J.JNT.2018.04.012zbMath1444.11180arXiv1708.07998OpenAlexW2963797523WikidataQ101170288 ScholiaQ101170288MaRDI QIDQ1786683

William Duke, Eric D'Hoker

Publication date: 24 September 2018

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.07998

zbMATH Keywords

modular graph functions

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items (16)

Zero mode of the Fourier series of some modular graphs from Poincaré series ⋮ Towards closed strings as single-valued open strings at genus one ⋮ Scalar‐valued depth two Eichler–Shimura integrals of cusp forms ⋮ Two string theory flavours of generalised Eisenstein series ⋮ To the cusp and back: resurgent analysis for modular graph functions ⋮ A simplifying feature of the heterotic one loop four graviton amplitude ⋮ Modular graph forms from equivariant iterated Eisenstein integrals ⋮ Generating series of all modular graph forms from iterated Eisenstein integrals ⋮ Higher genus modular graph functions, string invariants, and their exact asymptotics ⋮ Discreteness and integrality in conformal field theory ⋮ Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers ⋮ Integrating three-loop modular graph functions and transcendentality of string amplitudes ⋮ Poincaré series for modular graph forms at depth two. I: Seeds and Laplace systems ⋮ Poincaré series for modular graph forms at depth two. II: Iterated integrals of cusp forms ⋮ Basis decompositions and a Mathematica package for modular graph forms ⋮ The SAGEX review on scattering amplitudes Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their N=4 supersymmetric Yang–Mills duals

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