论文信息 - New asymptotic formulas for the distribution of left ideals of orders.

New asymptotic formulas for the distribution of left ideals of orders.

where X ranges over all left ideals of Λ which are isomorphic to M s Λ-modules. Landau's theorem gives an asymptotic formula of the required type for the partial sums of the coefficients of a (generalised) Dirichlet series, provided that the series satisfies a certain long list of hypotheses. The main group of these hypotheses demands that the series be continuable to a meromorphic function on the whole s-plane, and that it satisfy a certain functional equation. Such results for the series ΖΛ(Μ, s) are available from [6].

I. Reiner | C. Bushnell

[1] I. Reiner,et al. Functional equations for Hurwitz series and partial zeta functions of orders. , 1986 .

[2] I. Reiner,et al. Analytic continuation of partial zeta functions of arithmetic orders. , 1984 .

[3] I. Reiner,et al. The prime ideal theorem in non-commutative arithmetic , 1982 .

[4] Colin J. Bushnell,et al. L-functions of arithmetic orders and asymptotic distribution of ideals. , 1981 .

[5] I. Reiner,et al. Zeta functions of arithmetic orders and Solomon's conjectures , 1980 .

[6] A. Fröhlich. Locally free modules over arithmetic orders. , 1975 .

[7] E. Landau,et al. Ausgewählte Abhandlungen zur Gitterpunktlehre , 1962 .

[8] E. Landau,et al. Über die Anzahl der Gitterpunkte in geweissen Bereichen , 1912 .