We construct a -adic Eisenstein measure with values in the space of vector-weight -adic automorphic forms on certain unitary groups. This measure allows us to -adically interpolate special values of certain vector-weight automorphic forms, including Eisenstein series, as their weights vary. This completes a key step toward the construction of certain -adic -functions.
We also explain how to extend our methods to the case of Siegel modular forms and how to recover Nicholas Katz’s -adic families of Eisenstein series for Hilbert modular forms.
"A $p$-adic Eisenstein measure for vector-weight automorphic forms." Algebra Number Theory 8 (10) 2433 - 2469, 2014. https://doi.org/10.2140/ant.2014.8.2433