Panchishkin, Alexei Graded structures and differential operators on nearly holomorphic and quasimodular forms on classical groups. (English) Zbl 1424.11096 Sarajevo J. Math. 12(25), No. 2, Suppl., 401-417 (2016). Summary: We wish to use Krasner graded and Krasner-Vuković paragraded structures [M. Krasner, in: Algebra Colloquium. Rennes: Univ. Rennes. 209–308 (1980; Zbl 0521.16001); M. Krasner and M. Vuković, Structures paragraduées (groupes, anneaux, modules). (Paragraded structures (groups, rings, modules)). Ontario, Canada: Queen’s University Press (1987; Zbl 0624.08001); M. Vuković, “Structures graduées et paragraduées”, Prépublication de l’Institut Fourier, No. 536 (2001)] on differential 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 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 \(L(s, \pi, r, \chi)\).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. Cited in 1 Document MSC: 11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols 11F85 \(p\)-adic theory, local fields 11F33 Congruences for modular and \(p\)-adic modular forms 14G20 Local ground fields in algebraic geometry 22E50 Representations of Lie and linear algebraic groups over local fields 16W50 Graded rings and modules (associative rings and algebras) 16E45 Differential graded algebras and applications (associative algebraic aspects) Keywords:graded structures; automorphic forms; classical groups; \(p\)-adic \(L\)-functions; differential operators; non-Archimedean weight spaces; quasi-modular forms; Fourier coefficients Citations:Zbl 0521.16001; Zbl 0624.08001 PDFBibTeX XMLCite \textit{A. Panchishkin}, Sarajevo J. Math. 12(25), No. 2, 401--417 (2016; Zbl 1424.11096) Full Text: arXiv