The quest for a functional equation of L-functions in Drinfeld theory – Giacomo Hermes Ferraro (Sapienza Università di Roma)


Aula Seminari - Dipartimento di Matematica


The theory of Drinfeld modules, pioneered by Anderson and Thakur in the 90’s, was conceived as a possible analogue to the theory of complex elliptic curves in finite characteristic, where the role of the ring of integers $\mathbb{Z}$ is assumed by the ring of regular functions of some curve $X/F_q$. We will introduce the analogues of the real and complex numbers, of the period lattices, and of the exponential map in this context.

Two novel objects – special functions and Pellarin L-functions – arise in this theory, which have no parallel in characteristic zero, and can be conceived as interpolations of Gauss sums and Dirichlet L-functions, respectively; we will present some results about their relation, and compare them to the classical functional equation for Dirichlet L-functions.

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