Tate conjecture for twisted Siegel modular threefolds
The Arithmetic Genus of the Hubert Modular Variety and the Elliptic Fixed Points of the Hilbert Modular Group.
The Eichler Commutation Relation for theta series with spherical harmonics
It is well known that classical theta series which are attached to positive definite rational quadratic forms yield elliptic modular forms, and linear combinations of theta series attached to lattices in a fixed genus can yield both cusp forms and Eisenstein series whose weight is one-half the rank of the quadratic form. In contrast, generalized theta series - those augmented with a spherical harmonic polynomial - will always yield cusp forms whose weight is increased by the degree of the...
The Fixed Points of the Symmetrie Hilbert Modular Group of a Real Quadratic Field with Arbitrary Discriminant.
The Hilbert Modular Group for the Field ...(...13).
The Hilbert modular group, resolution of the singularities at the cusps and related problems
The Hilbert Modular Surface for the Ideal (...5) and the Horrocks-Mumford Bundle.
The level 1 weight 2 case of Serre's conjecture.
The Strong Rigidity of Locally Symmetric Complex Manifolds of Rank One and Finite Volume.
Theta correspondence and Hecke operators relative to a quadratic extension
Theta functions of quadratic forms over imaginary quadratic fields
1. Introduction. Let Q be a positive definite n × n matrix with integral entries and even diagonal entries. It is well known that the theta function , Im z > 0, is a modular form of weight n/2 on , where N is the level of Q, i.e. is integral and has even diagonal entries. This was proved by Schoeneberg [5] for even n and by Pfetzer [3] for odd n. Shimura [6] uses the Poisson summation formula to generalize their results for arbitrary n and he also computes the theta multiplier explicitly....
Theta Series of a Real Algebraic Number Fields.
Thetafunctionen und symmetrische Hilbertsche Modulformen zu ... (...).
Thetareihen und modulare Spitzenformen zu den Hilbertschen Modulgruppen reell-quadratischer Körper.
Thetareihen und modulare Spitzenformen zu den Hilbertschen Modulgruppen reell-quadratischer Körper. II.
Transgressed Euler classes of vector bundles, adiabatic limits of eta invariants and special values of -functions
Tsuchihashi's Cusp Singularities and Automorphisms of Hilbert Modular Variety Cusps.