Special values of shifted convolution Dirichlet series

In a recent important paper, Hoffstein and Hulse generalized
the notion of Rankin-Selberg convolution L-functions by defining shifted
convolution L-functions. We investigate symmetrized versions of their
functions, and we prove that the generating functions of certain special
values are linear combinations of weakly holomorphic quasimodular forms
and ``mixed mock modular'' forms. If there is time, we also investigate
p-adic properties of these special values.
This is joint work with Ken Ono and Kathrin Bringmann.