Kurchanov, P. F. Local measures related with parabolic Jacquet-Langlands forms over CM-fields. (Russian) Zbl 0417.12004 Mat. Sb., N. Ser. 108(150), 483-503 (1979). This paper is closely connected with the paper written by Yu. I. Manin in [Usp. Mat. Nauk 31, No. 1(187), 5–54 (1976; Zbl 0336.12007) and devoted to the construction of \(p\)-adic analogy of \(L\)-functions of modular forms. These functions were connected with representations of \(\mathrm{GL}(2)\) over totally real fields. In the present paper Manin’s construction is generalized on CM-fields. The author investigates all over again Manin’s formula for a local measure and then he interprets the main arithmetical functions of the measure formula as periods of a closed differential form on a variety with unique singularity. The main theorem is devoted to establish estimates for some measures. Reviewer: A. A. Bel’skiĭ (Moskva) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 2 Documents MSC: 11S40 Zeta functions and \(L\)-functions 11S85 Other nonanalytic theory 20G05 Representation theory for linear algebraic groups 11G15 Complex multiplication and moduli of abelian varieties Keywords:parabolic Jacquet-Langlands forms; CM-fields; p-adic L-functions of modular forms; representations of GL(2) Citations:Zbl 0336.12007 PDFBibTeX XMLCite \textit{P. F. Kurchanov}, Mat. Sb., Nov. Ser. 108(150), 483--503 (1979; Zbl 0417.12004) Full Text: EuDML