Let p be a rational prime, q>1 a p-power and P a non-constant irreducible polynomial in F_q[t]. The notion of Drinfeld modular form is an analogue over F_q(t) of that of elliptic modular form. On the other hand, following the analogy with p-adic elliptic modular forms, Vincent defined P-adic Drinfeld modular forms as the P-adic limits of Fourier expansions of Drinfeld modular forms. Numerical computations suggest that Drinfeld modular forms should enjoy deep P-adic structures comparable to the elliptic analogue, while at present their P-adic properties are far less well understood than the p-adic elliptic case.
In this talk, I will explain how basic properties of P-adic Drinfeld modular forms are obtained from the duality theories of Taguchi for Drinfeld modules and finite v-modules. |