Christopher Williams (University of Warwick):

Overconvergent Bianchi modular symbols and p-adic L-functions

Abstract: Modular symbols are powerful algebraic tools in the study of modular forms. Pollack and Stevens used overconvergent modular symbols to give a beautiful and effective construction of the p-adic L-function of a classical modular form. In particular, they used Stevens' control theorem - a modular symbol analogue of Coleman's small slope classicality theorem - to attach a canonical overconvergent modular symbol to a small slope classical eigenform. The p-adic L-function can then be constructed from this overconvergent symbol in a natural way. In this talk, I will describe their results, before discussing an analogue over imaginary quadratic fields, constructing a p-adic L-function for any small slope Bianchi modular form.

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