Characteristic Classes of Kuga Fiber Varieties of Quaternion Type.
On the Kronecker Pairing for Mixed Cusp Forms.
Periods of Mixed Cusp Forms.
Cohen-Kuznetsov liftings of quasimodular forms
Jacobi-like forms for a discrete subgroup Γ of SL(2,ℝ) are formal power series which generalize Jacobi forms, and they correspond to certain sequences of modular forms for Γ. Given a modular form f, a Jacobi-like form can be constructed by using constant multiples of derivatives of f as coefficients, which is known as the Cohen-Kuznetsov lifting of f. We extend Cohen-Kuznetsov liftings to quasimodular forms by determining an explicit formula for a Jacobi-like form associated to a quasimodular form....
Twisted modular forms and parabolic cohomology
Quasimodular forms and Poincaré series
Hecke operators on de Rham cohomology.
We introduce Hecke operators on de Rham cohomology of compact oriented manifolds. When the manifold is a quotient of a Hermitian symmetric domain, we prove that certain types of such operators are compatible with the usual Hecke operators on automorphic forms.
Eisenstein series and Poincaré series for mixed automorphic forms.
Mixed automorphic forms generalize elliptic modular forms, and they occur naturally as holomorphic forms of the highest degree on families of abelian varieties parametrized by a Riemann surface. We construct generalized Eisenstein series and Poincaré series, and prove that they are mixed automorphic forms.
Generalized Jacobi forms and abelian schemes over arithmetic varieties.
We generalize Jacobi forms of an arbitrary degree and construct torus bundles over abelian schemes whose sections can be identified with such generalized Jacobi forms.
Lie algebras of formal power series.
Quasimodular forms and quasimodular polynomials
This paper is based on lectures delivered at the Workshop on quasimodular forms held in June, 2010 in Besse, France, and it provides a survey of some recent work on quasimodular forms.
Vector-valued modular forms associated to linear ordinary differential equations
We consider a class of linear ordinary differential equations determined by a modular form of weight one, and construct vector-valued modular forms of weight two by using solutions of such differential equations.
Hecke operators on the -analogue of group cohomology.
Jacobi forms on symmetric domains and torus bundles over Abelian schemes.
Mixed automorphic forms and differential equations.
Fourier coefficients of Hilbert cusp forms associated with mixed Hilbert cusp forms.
Mixed Jacobi-like forms of several variables.
Cohomology of torus bundles over Kuga fiber varieties.
On the monotonicity of the quotient of certain abelian integrals.
Casimir operators on pseudodifferential operators of several variables.
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