  We wish to use graded structures [KrVu87], [Vu01] on dffierential operators
and quasimodular forms on classical groups and show that these structures
provide a tool to construct p-adic measures and p-adic L-functions on the
corresponding non-archimedean weight spaces. An approach to constructions of
automorphic L-functions on uni-tary groups and their p-adic avatars is
presented. For an algebraic group G over a number eld K these L functions are
certain Euler products L(s, $\pi$, r, $\chi$). In particular, our constructions
cover the L-functions in [Shi00] via the doubling method of Piatetski-Shapiro
and Rallis. A p-adic analogue of L(s, $\pi$, r, $\chi$) is a p-adic analytic
function L p (s, $\pi$, r, $\chi$) of p-adic arguments s $\in$ Z p , $\chi$ mod
p rPresented in a talk for the INTERNATIONAL SCIENTIFIC CONFERENCE "GRADED
STRUCTURES IN ALGEBRA AND THEIR APPLICATIONS" dedicated to the memory of Prof.
Marc Krasner on Friday, September 23, 2016, International University Centre
(IUC), Dubrovnik, Croatia.
