Holomorphic Automorphic Forms and Cohomology

DOI10.1090/memo/1212zbMath1470.11119arXiv1404.6718OpenAlexW4214571484WikidataQ130028694 ScholiaQ130028694MaRDI QIDQ4645839

Nikolaos Diamantis, Young Ju Choie, Roelof Wichert Bruggeman

Publication date: 11 January 2019

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.6718

zbMATH Keywords

cohomologyharmonic functionsEichler integralperiod functionharmonic liftholomorphic automorphic formboundary germmixed parabolic cohomology

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Automorphic forms, one variable (11F12) Cohomology of arithmetic groups (11F75)

Related Items

Limit laws for rational continued fractions and value distribution of quantum modular forms, Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume, Finite-dimensional period spaces for the spaces of cusp forms, The Eichler-Shimura cohomology theorem for Jacobi forms, Modular cocycles and cup product, Limits of traces of singular moduli, Convergence of Poincaré series on Hecke groups of large width, Eichler cohomology in general weights using spectral theory, Parabolic cohomology and multiple Hecke \(L\)-values, Ramanujan identities of higher degree, Modular forms of real weights and generalised Dedekind symbols, Holomorphic modular forms and cocycles, A class of non-holomorphic modular forms. I, Period polynomials, derivatives of \(L\)-functions, and zeros of polynomials, Special values of Hecke \(L\)-functions of modular forms of half-integral weight and cohomology, Maass wave forms, quantum modular forms and Hecke operators

Cites Work

• Period Functions for Maass Cusp Forms for Γ0(p): A Transfer Operator Approach
• Lifting cusp forms to Maass forms with an application to partitions
• A Lewis Correspondence for submodular groups
• Derivation and double shuffle relations for multiple zeta values
• The Eichler Cohomology Groups and Automorphic Forms
• Grenzkreisgruppen und kettenbruchartige Algorithmen
• Automorphic integrals with preassigned periods
• Construction of Automorphic Forms on H-Groups and Supplementary Fourier Series
• Period functions for Maass wave forms. I.
• The heat operator and mock Jacobi forms
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Period functions of half-integral weight modular forms
• Eichler integrals for Maass cusp forms of half-integral weight
• Evaluation of the multiple zeta values \(\zeta(2,\ldots,2,3,2,\ldots,2)\)
• Eichler integrals, period relations and Jacobi forms
• Rational period functions and cycle integrals
• Lewis-Zagier correspondence for higher-order forms
• Mellin transforms attached to certain automorphic integrals
• Eine Verallgemeinerung der Abelschen Integrale
• On integrals attached to automorphic forms
• Hecke-Integrale mit rationalen periodischen Funktionen und Dirichlet-Reihen mit Funktionalgleichung
• A Hecke correspondence theorem for automorphic integrals with rational period functions
• Periods of modular forms of weight one
• Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues
• Rational period functions for the modular group and real quadratic fields
• Rational period functions and indefinite binary quadratic forms. I
• Periods of modular forms and Jacobi theta functions
• Rational period functions, class numbers, and diophantine equations
• Weil's representation and the spectrum of the metaplectic group
• Rational period functions of the modular group. (Appendix by Georges Grinstein)
• Power series and asymptotic series associated with the Lerch zeta-function
• Hecke operators on rational period functions on the Hecke groups
• Spaces of holomorphic functions equivalent to the even Maass cusp forms
• Modular forms, generalized Dedekind symbols and period polynomials
• On two geometric theta lifts
• Automorphic forms on \(O_{s+2,2}(\mathbb R)\) and infinite products
• Generalized modular forms.
• Rational period functions and parabolic cohomology
• Invariants, cohomology, and automorphic forms of higher order
• Mock period functions, sesquiharmonic Maass forms, and non-critical values of \(L\)-functions
• Higher-order Maass forms
• A dynamical approach to Maass cusp forms
• Eichler-Shimura theory for mock modular forms
• On the Hurwitz-Lerch zeta-function.
• Eigenfunctions of transfer operators and cohomology
• Harmonic lifts of modular forms
• Weak Maass-Poincaré series and weight 3/2 mock modular forms
• Values of \(L\)-functions at integers outside the critical strip
• Regularized inner products of modular functions
• Note on automorphic forms with real period polynomials
• Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I, II. (The eigenvalue problem of automorphic forms in the hyperbolic plane. I. II)
• The Plancherel formula for the universal covering group of SL(R, 2)
• On cohomology of Kleinian groups. II
• Factors of automorphy and other formal cohomology groups for Lie groups
• On cohomology of Kleinian groups
• Eichler cohomology and automorphic forms
• Cohomology of arithmetic groups with infinite dimensional coefficient spaces
• Rational period functions and indefinite binary quadratic forms. II
• Invarianten linearer Differentialgleichungen
• Odd and even Maass cusp forms for Hecke triangle groups, and the billiard flow
• Higher Kronecker “limit” formulas for real quadratic fields
• On a completed generating function of locally harmonic Maass forms
• The Lerch zeta function II. Analytic continuation
• Perioden von Modulformen einer Variabler und Gruppencohomologie, I
• A decomposition of the space of higher order modular cusp forms
• Variational Property of Cusp Forms
• The thermodynamic formalism approach to Selberg’s zeta function for 𝑃𝑆𝐿(2,𝐙)
• The dimensions of spaces of holomorphic second-order automorphic forms and their cohomology
• Higher order group cohomology and the Eichler-Shimura map
• EICHLER COHOMOLOGY FOR GENERALIZED MODULAR FORMS
• Eichler-Shimura Homology, Intersection Numbers and Rational Structures on Spaces of Modular Forms
• Parabolic Cohomology of Arithmetic Subgroups of SL(2, Z ) with Coefficients in the Field of Rational Functions on the Riemann Sphere
• Rational period functions of the modular group II
• Some new results on the Eichler cohomology of automorphic forms
• Construction of Automorphic Forms and Integrals
• The theory of Hecke integrals
• Fourier coefficients of the resolvent for a Fuchsian group.
• Modular Forms for Γ 0 (N) and Dirichlet Series
• Special values of higher derivatives of L-functions
• The space of period polynomials
• Automorphic forms, hyperfunction cohomology, and period functions.
• Resolutions of distribution globalizations of HarishChandra modules and cohomology
• The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, II
• Fractional integrals of modular forms
• The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, I
• A class of nonanalytic automorphic functions
• $\Gamma$-Cohomology and the Selberg Zeta Function
• Eichler cohomology of generalized modular forms of real weights
• Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant
• Function Theory Related to the Group PSL2(ℝ)
• EICHLER COHOMOLOGY FOR GENERALIZED MODULAR FORMS II
• Eichler cohomology theorem for automorphic forms of small weights
• EICHLER COHOMOLOGY THEOREM FOR GENERALIZED MODULAR FORMS