Nonvanishing theorems for twisted L-functions on unitary groups. (Previously cited as Nonvanishing of central values of twisted L-functions.) Submitted. For most recent version (updated August 16, 2017), click on title above. For (older) arXiv version, visit http://arxiv.org/pdf/1708.04026.pdf. This paper demonstrates how new results on nonvanishing can be obtained by combining decades-old methods from Iwasawa theory with the output of new machinery.
p-adic L-functions for unitary groups. With M. Harris, J.-S. Li, and C. Skinner. 135 pages. Submitted. This paper completes the construction of p-adic L-functions for unitary groups. It contains both Part II and Part III.
For an overview of the key ingredients in the construction, I recommend these slides: slides