The space of elliptic modular forms of fixed weight and level can be identified with a space of intertwining operators, from a holomorphic discrete series representation of SL2(R) to a space of automorphic forms. Moreover, multiplying elliptic modular forms corresponds to a branching problem involving tensor products of holomorphic discrete series representations. In this paper, we explicitly c...

1 Hilbert modular surfaces 3 1.1 The Hilbert modular group . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 The Baily-Borel compactification . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Siegel domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Hilbert modular forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Mk(Γ) is finite dimensional...

Digital multimedia such as images and videos are prevalent on today’s internet and cause significant social impact, which can be evidenced by the proliferation of social networking sites with user generated contents. Due to the ease of generating and modifying images and videos, it is critical to establish trustworthiness for online multimedia information. In this paper, we propose a new framew...

FDBG (short for Finite domain DeBuGger) is a tool addressing the problems of debugging nite domain (FD) constraint programs. Implemented as a SICStus Prolog library, it allows CLP(FD) programmers to trace FD variable domain changes. FDBG is capable of detecting the wake-up of constraints as well as the steps of labeling, and it reports the e ects of these events on the variables. The simplest w...