A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS

DOI10.1017/fms.2020.24zbMath1452.11054arXiv1708.03354OpenAlexW3030573646MaRDI QIDQ3294956

Francis C. S. Brown

Publication date: 29 June 2020

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.03354

zbMATH Keywords

modular formsEisenstein integralsnon-holomorphic modular forms

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items (26)

Modular iterated integrals associated with cusp forms ⋮ Towards closed strings as single-valued open strings at genus one ⋮ Two dialects for KZB equations: generating one-loop open-string integrals ⋮ Laplace-eigenvalue equations for length three modular iterated integrals ⋮ All-order differential equations for one-loop closed-string integrals and modular graph forms ⋮ Modular graph functions and odd cuspidal functions. Fourier and Poincaré series ⋮ 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 ⋮ Modular graph forms from equivariant iterated Eisenstein integrals ⋮ Period functions associated to real-analytic modular forms ⋮ Generating series of all modular graph forms from iterated Eisenstein integrals ⋮ Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings ⋮ Holomorphic subgraph reduction of higher-point modular graph forms ⋮ From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop ⋮ Higher genus modular graph functions, string invariants, and their exact asymptotics ⋮ Elliptic modular graph forms. I: Identities and generating series ⋮ Fourier series of modular graph functions ⋮ Diagrammatic expansion of non-perturbative little string free energies ⋮ Coaction and double-copy properties of configuration-space integrals at genus zero ⋮ Exploring transcendentality in superstring amplitudes ⋮ Vector-valued higher depth quantum modular forms and higher Mordell integrals ⋮ One-loop matrix elements of effective superstring interactions: \(\alpha^\prime\)-expanding loop integrands ⋮ 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 ⋮ 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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Kernels for products of \(L\)-functions
• Eine Verallgemeinerung der Abelschen Integrale
• On integrals attached to automorphic forms
• Hierarchy of modular graph identities
• On the algebraic structure of iterated integrals of quasimodular forms
• Identities between modular graph forms
• Single-valued multiple polylogarithms in one variable
• On some derivations of Lie algebras related to Galois representations
• Notes on the universal elliptic KZB connection
• A class of non-holomorphic modular forms. I
• A class of non-holomorphic modular forms. III: real analytic cusp forms for \(\mathrm{SL}_2(\mathbb{Z})\)
• Single-valued multiple zeta values in genus \(1\) superstring amplitudes
• Elliptic associators
• ZETA ELEMENTS IN DEPTH 3 AND THE FUNDAMENTAL LIE ALGEBRA OF THE INFINITESIMAL TATE CURVE
• The Hodge-de~Rham Theory of Modular Groups
• Elliptic Modular Forms and Their Applications
• Projections of 𝐶^{∞} automorphic forms
• PERIODS OF PARABOLIC FORMS AND $ p$-ADIC HECKE SERIES
• Iterated path integrals
• The hodge de rham theory of relative malcev completion1
• Universal KZB Equations: The Elliptic Case
• UNIVERSAL MIXED ELLIPTIC MOTIVES
• Iterated integrals of modular forms and noncommutative modular symbols
• Derivation and double shuffle relations for multiple zeta values
• Depth-graded motivic multiple zeta values

This page was built for publication: A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS