  Let F be a global field and A its ring of adeles. Let G:=SL(2). We study the
bilinear form B on the space of K-finite smooth compactly supported functions
on G(A )/G(F) defined by the formula B (f,g):=B'(f,g)-(M^{-1}CT (f),CT (g)),
where B' is the usual scalar product, CT is the constant term operator, and M
is the standard intertwiner. This form is natural from the viewpoint of the
geometric Langlands program. To justify this claim, we provide a dictionary
between the classical and "geometric" theory of automorphic forms. We also show
that the form B is related to S. Schieder's Picard-Lefschetz oscillators.
