Graded Structures and Differential Operators on Nearly Holomorphic and Quasimodular Forms on Classical Groups

We wish to use Krasner graded and Krasner-Vukovi´paragraded structures on differential operators and quasimod-ular forms on classical groups and show that these structures provide a tool to construct p-adic measures and p-adic L-functions on the corre-sponding non-archimedean weight spaces. An approach to constructions of automorphic L-functions on unitary groups and their p-adic analogues is presented. For an algebraic group G over a number field K these L functions are certain Euler products L(s, π, r, χ). We present a method using arithmetic nearly-holomorphic forms and general quasi-modular forms, related to algebraic automorphic forms. It gives a technique of constructing p-adic zeta-functions via quasi-modular forms and their Fourier coefficients. * This paper was presented at the International Scientific Conference Graded structures in algebra and their applications, dedicated to the memory of Prof. Marc Krasner, IUCDubrovnik, Cratia, September, 22-24, 2016.