Panchishkin, A. A. The Maass-Shimura differential operators and congruences between arithmetical Siegel modular forms. (English) Zbl 1129.11021 Mosc. Math. J. 5, No. 4, 863-918 (2005). The author studies congruences between nearly holomorphic Siegel modular forms using an explicit action of the Maass-Shimura arithmetical differential operators. \(p\)-adic congruences between these forms produce various \(p\)-adic \(L\)-functions using a general method of canonical projection. A general construction of \(h\)-admissible measures attached to sequences of special modular distributions is stated in section 5 (Theorem 5.1). This construction includes (as special cases) the standard \(L\)-functions of Siegel cusp forms (of small slope) and \(L\)-functions of elliptic cusp forms. Reviewer: Andrzej Dąbrowski (Szczecin) Cited in 4 Documents MSC: 11F60 Hecke-Petersson operators, differential operators (several variables) 11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols 11F85 \(p\)-adic theory, local fields 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms Keywords:Hecke operators; Siegel-Eisenstein series; \(h\)-admissible measures PDFBibTeX XMLCite \textit{A. A. Panchishkin}, Mosc. Math. J. 5, No. 4, 863--918 (2005; Zbl 1129.11021)