A class of non-holomorphic modular forms. III: real analytic cusp forms for \(\mathrm{SL}_2(\mathbb{Z})\)

DOI10.1007/s40687-018-0151-3zbMath1440.11071arXiv1710.07912OpenAlexW2963781503MaRDI QIDQ2319766

Francis C. S. Brown

Publication date: 20 August 2019

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.07912

zbMATH Keywords

mock modular formsreal analytic cusp forms

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37)

Related Items

Modular iterated integrals associated with cusp forms ⋮ Laplace-eigenvalue equations for length three modular iterated integrals ⋮ Algebraic de Rham theory for the relative completion of 𝑆𝐿₂(ℤ) ⋮ Period functions associated to real-analytic modular forms ⋮ On coefficients of Poincaré series and single-valued periods of modular forms ⋮ Generating series of all modular graph forms from iterated Eisenstein integrals ⋮ A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS ⋮ Discreteness and integrality in conformal field theory ⋮ Single-valued integration and double copy ⋮ Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers ⋮ A class of non-holomorphic modular forms. I ⋮ Poincaré series for modular graph forms at depth two. II: Iterated integrals of cusp forms ⋮ Empirical Determinations of Feynman Integrals Using Integer Relation Algorithms ⋮ 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

Cites Work

• Unnamed Item
• Harmonic weak Maass forms of integral weight: a geometric approach
• A geometric perspective on \(p\)-adic properties of mock modular forms
• On integrals attached to automorphic forms
• Lectures on modular functions of one complex variable. Notes by Sunder Lal. Rev. ed
• Modular forms and de Rham cohomology; Atkin-Swinnerton-Dyer congruences
• Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues
• Elliptic functions and transcendence
• On the periods of modular forms
• Algebraic de Rham theory for weakly holomorphic modular forms of level one
• Notes on motivic periods
• On two geometric theta lifts
• Motives for modular forms
• Eichler-Shimura theory for mock modular forms
• A class of non-holomorphic modular forms. I
• Invarianten linearer Differentialgleichungen
• Modular forms, de Rham cohomology and congruences
• The Hodge-de~Rham Theory of Modular Groups
• Hecke operators for weakly holomorphic modular forms and supersingular congruences
• A Mock Theta Function for the Delta-function
• PERIODS OF PARABOLIC FORMS AND $ p$-ADIC HECKE SERIES
• Lifting cusp forms to Maass forms with an application to partitions
• Classical and overconvergent modular forms