Theta function transformation formulas and the Weil representation

Theta Series Associated with the Schrödinger-weil Representation

In this paper, we define the Schrödinger-Weil representation for the Jacobi group and construct covariant maps for the Schrödinger-Weil representation. Using these covariant maps, we construct Jacobi forms with respect to an arithmetic subgroup of the Jacobi group.

The Weil Representation

This is my senior honors thesis done in my final year as an undergraduate at Stanford University, under the direction of Professor Akshay Venkatesh. We will construct the Weil representation of SL2(R) through a natural action of the Heisenberg group Heis(R) on the space of square-integrable complex-valued functions L 2(R), together with the celebrated Stone-von Neumann theorem of functional ana...

M ay 2 00 9 HEISENBERG GROUPS , THETA FUNCTIONS AND THE WEIL REPRESENTATION

Random 3CNF formulas elude the Lovasz theta function

Let φ be a 3CNF formula with n variables and m clauses. A simple nonconstructive argument shows that when m is sufficiently large compared to n, most 3CNF formulas are not satisfiable. It is an open question whether there is an efficient refutation algorithm that for most such formulas proves that they are not satisfiable. A possible approach to refute a formula φ is: first, translate it into a...

Transformation Formula of the “2nd” Order Mock Theta Function

KAZUHIRO HIKAMI A. We give a transformation formula for the " 2nd order " mock theta function D 5 (q) = ∞ n=0 (−q) n (q; q 2) n+1 q n which was recently proposed in connection with the quantum invariant for the Seifert manifold.