Related papers: A Note on Maass-Jacobi Forms

In this paper, we introduce the concept of stable automorphic forms for semisimple algebraic groups and use the stability of automorphic forms to study the geometry of infinite dimensional arithmetic quotients.

The Jacobi group is the semi-direct product of the symplectic group and the Heisenberg group. The Jacobi group is an important object in the framework of quantum mechanics, geometric quantization and optics. In this paper, we study the Weil…

Kohnen introduced a limit process for Siegel modular forms that produces Jacobi forms. He asked if there is a space of real-analytic Siegel modular forms such that skew-holomorphic Jacobi forms arise via this limit process. In this paper,…

By modifying a slash operator of index zero we define \textit{modified Jacobi forms} of \textit{index zero}. Such forms play a role of generating nearly holomorphic modular forms of integral weight. Furthermore, by observing a relation…

We reformulate the notion of a Jacobi algebroid in terms of weighted odd Jacobi brackets. We then show how a Jacobi algebroid can be understood in terms of a kind of curved Q-manifold. In particular the homological condition on the odd…

In this paper we present our variant of quantum antisymmetry and quantum Jacobi identity.

Motivated by issues in string theory and M-theory, we provide a pedestrian introduction to automorphic forms and theta series, emphasizing examples rather than generality.

This paper gives a technically elementary treatment of some aspects of Hamilton-Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the application to geometric optics, the…

We give archimedean and non-archimedean constructions of Darmon points on modular abelian varieties attached to automorphic forms over arbitrary number fields and possibly non-trivial central character. An effort is made to present a…

A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.

The purpose of this review paper is the collection, systematization and discussion of recent results concerning the quantization approach to the Jacobian conjecture, as well as certain related topics.

Eichler and Zagier developed a theory of Jacobi forms to understand and extend Maass' work on the Saito-Kurokawa conjecture. Later Skoruppa introduced skew-holomorphic Jacobi forms, which play an important role in understanding liftings of…

This note documents the specification of normal forms in cubical type theory. The definition is already present in the proof of normalization for cubical type theory, but we present it in a more traditional style explicitly for reference.

We study twisted Jacobi manifolds, a concept that we had introduced in a previous Note. Twisted Jacobi manifolds can be characterized using twisted Dirac-Jacobi, which are sub-bundles of Courant-Jacobi algebroids. We show that each twisted…

This is an informal and mostly expository note describing some asymptotic behavior and qualitative properties of the q-binomial coefficients. The results are mostly not new, but the overall story we present does not seem to be well known --…

The geometric properties of sigma models with target space a Jacobi manifold are investigated. In their basic formulation, these are topological field theories - recently introduced by the authors - which share and generalise relevant…

In this paper we develop a Hamilton-Jacobi theory in the setting of almost Poisson manifolds. The theory extends the classical Hamilton-Jacobi theory and can be also applied to very general situations including nonholonomic mechanical…

We utilize the structure of quasiautomorphic forms over an arbitrary Hecke triangle group to define a new vector analogue of an automorphic form. We supply a proof of the functional equations that hold for these functions modulo the group…

In this paper we define a Grassmann odd analogue of Jacobi structure on a supermanifold. The basic properties are explored. The construction of odd Jacobi manifolds is then used to reexamine the notion of a Jacobi algebroid. It is shown…

The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also, several basic properties of group-groupoids are established.