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# Texas A&M Number Theory Seminar

##
Department of Mathematics

Blocker 220

Wednesdays, 1:45–2:45 PM

### Shin Hattori

Kyushu University

#### Wednesday, December 6, 2017

#### Blocker 220, 1:45PM

**Title:** *Duality of Drinfeld modules and P-adic properties of Drinfeld modular forms
*

**Abstract:**
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.