In this paper, using a matrix summability method we obtain a Korovkin type approximation theorem for a sequence of positive linear operators defined on a modular space.

We state a result and describe an algorithm for computing the intersection number between abelian varieties associated to complementary subspaces of the space of cuspidal modular forms.

We explicitly compute the elliptic points and isotropy groups for the action of the Picard modular group over the Gaussian integers on 2-dimensional complex hyperbolic space.

In this thesis, we set up the basic theory of p-adic modular forms over Shimura curves over Q, parallel to the classical case over modular curves. We define and study the structure of the spaces of p-adic modular forms with respect to certain quaternion algebras over Q. We study the relation of these modular forms with classical quaternionic modular forms. We prove a canonical subgroup theorem ...

Our main goal is to analyze the geometric and spectral properties of the Picard modular group with Gaussian integer entries acting on the two-dimensional complex hyperbolic space.

Let M (n) k be the space of Siegel modular forms of degree n and even weight k. In this paper firstly a certain subspace Spez(M (2n) k ) the Spezialschar of M (2n) k is introduced. In the setting of the Siegel three-fold it is proven that this Spezialschar is the Maass Spezialschar. Secondly an embedding of M (2) k into a direct sum ⊕ ⌊ k 10 ⌋ ν=0 Sym 2 Mk+2ν is given. This leads to a basic cha...

Introduction: Orlicz and Birnbaum considered spaces of functions with growth properties different from the power type growth control, provided by the p L -norm. This generalization found many applications in differential and integral equations with kernels of non-power types. A more abstract approach was given by Nakano in connection with the theory of order spaces. His point of view was genera...

Target space modular symmetries relevant to string loop threshold corrections are studied for Z N orbifold compactified string theories containing Wilson line background fields.

In a series of works [Bo3-5], Borcherds developed a theory of modular forms over domains of type IV which admits an infinite product expansion. Among such modular forms, Borcherds’s Φ-function ([Bo4]) has an interesting geometric background; It is a modular form on the moduli space of Enriques surfaces characterizing the discriminant locus. In his construction, Φ-function is obtained as the den...