Abstract Lennart Gehrmann

On $p$-adic $L$-functions for $\mathrm{GL}(2n)$

P-adic L-functions describe congruences between special values of complex L-series. After reviewing some of the classical examples of p-adic L-functions we give a construction of p-adic L-functions for certain cuspidal automorphic representations of GL(2n), which have a Shalika model. This generalizes a construction of Ash-Ginzburg. As a special case we construct p-adic L-functions for the symmetric cube of modular elliptic curves over totally real fields.