Let F be a locally compact non-Archimedean field, and let B/F be a division algebra of dimension 4. The JacquetLanglands correspondence provides a bijection between smooth irreducible representations π′ of B× of dimension > 1 and irreducible cuspidal representations of GL2(F ). We present a new construction of this bijection in which the preservation of epsilon factors is automatic. This is don...

In this article we obtain class invariants and cyclotomic unit groups by considering specializations of modular units. We construct these modular units from functional solutions to higher order q-recurrence equations given by Selberg in his work generalizing the Rogers-Ramanujan identities. As a corollary, we provide a new proof of a result of Zagier and Gupta, originally considered by Gauss, r...

For moduli space of stable parabolic bundles on a compact Riemann surface, we derive an explicit formula for the curvature of its canonical line bundle with respect to Quillen’s metric and interpret it as a local index theorem for the family of ∂̄-operators in associated parabolic endomorphism bundles. The formula consists of two terms: one standard (proportional to the canonical Kähler form on ...

A lifting map from cuspidal automorphic representations of the Jacobi group G J to cuspidal auto-morphic representations of the group PGL(2) is constructed. The lifting also has a local deenition, and the local and global versions are compatible. The local lifts can be described in terms of equivalence classes of local representations. The main idea in the construction is to exploit the close r...