Graded Structures and Differential Operators on Nearly Holomorphic and Quasimodular Forms on Classical Groups
DOI:
https://doi.org/10.5644/SJM.12.3.12Keywords:
Graded structures, automorphic forms, classical groups, p-adic L-functions, differential operators, non-archimedean weight spaces, quasi-modular forms, Fourier coefficientsAbstract
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.
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