%0 Journal Article
%T Cusp Eigenforms and the Hall Algebra of an Elliptic Curve
%A Dragos Fratila
%J Mathematics
%D 2011
%I arXiv
%R 10.1112/S0010437X12000784
%X We give an explicit construction of the cusp eigenforms on an elliptic curve defined over a finite field using the theory of Hall algebras and the Langlands correspondence for function fields and $\GL_n$. As a consequence we obtain a description of the Hall algebra of an elliptic curve as an infinite tensor product of simpler algebras. We prove that all these algebras are specializations of a universal spherical Hall algebra (as defined and studied in \cite{BS} and \cite{SV1}).
%U http://arxiv.org/abs/1109.4308v1