A UNIFYING PRINCIPAL IN QUANTIFICATION THEORY.

(APHpX)o(ApOX + p3X2)o(Ap1PIX). One may conjecture that a similar factorization of the denominator of Dp(s) holds also for n > 2; the degree of the factors would be n!/(J!(n -j)!) for 0 < j . n. l Eichler, M., "Quaternare quadratische Formen und die Riemannsche Vermutung fhr die Kongruenzzetafunktion," Arch. Math., 5, 355-366 (1954). 2 Shimura, G., "Correspondances modulaires et les fonctions r de courbes algdbriques," J. Math. Soc. Japan, 10, 1-28 (1958). 3 Shimura, G., "On the zeta-functions of the algebraic curves uniformized by certain automorphic functions," J. Math. Soc. Japan, 13, 275-331 (1961). 4 Shimura, G., "Sur les integrales attach6es aux formes automorphes," J. Math. Soc. Japan, 11, 291-311 (1959). 5 Shimura, G., "Arithmetic of alternating forms and quaternion hermitian forms," to appear in J. Math. Soc. Japan. 6 Hecke, E., "Uber Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung," I, II, Math. Ann., 114, 1-28, 316-351 (1937). 7 Cartan, S6minaire H., E.N.S. (1957-58) expos6s 18-20. 8 Shimura, G., "On analytic families of polarized abelian varieties and automorphic functions," to appear in Ann. Math. 9 Shimura, G.; "On the theory of automorphic functions," Ann. Math., 70, 101-144 (1959).