On some algebraic properties of CM-types of CM-fields and their reflexes

The purpose of this paper is to show that the reflex fields of a given CM-field is equipped with a certain combinatorial structure that has not been exploited yet. We prove three theorems using this structure; the first theorem is on the abelian extension generated by the moduli and the b-torsion points of abelian varieties of CM-type, for any natural number b. It is a generalization of the result by Wei on the abelian extension obtained by the moduli and all the torsion points. The second theorem gives a character identity of the Artin L-function of a CM-field K and the reflex fields of K. The character identity pointed out by Shimura follows from this. The third theorem states that some Pfister form is isomorphic to the orthogonal sum of Tr(\bar{a}a) (\bar{a} is the complex conjugation of a) defined on a direct sum of reflex fields. This result suggests that the theory of complex multiplication on abelian varieties has a relationship with the multiplicative forms in higher dimension

Sectoral Labor Income Share Dynamics: Cross-Country Evidence from a Novel Dataset

Despite steady growth of the literature on labor income share, empirical studies are mostly limited to country-level analyses. At the sectoral level, data on labor income share are available only for advanced countries. This paper overcomes this constraint and provides some preliminary outcomes from a novel dataset that the authors compile at the sectoral level (10 sectors) for 53 countries, including 20 developing countries. The preliminary evidence suggests that, at the disaggregated level, the government service sector accounts for the largest share of labor income (46%), whereas public utilities (16%) and mining (20%) are the sectors with the smallest shares of labor income. The unweighted average labor income share in developing countries is slightly lower than that in developed countries. We find considerable variation in labor income share estimates within each region and within each broad category of sectors, measured at the level and with changes over time

Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons

Background: Magnetic dipole (M1) excitation is the leading mode of nuclear excitation by the magnetic field, which couples unnatural-parity states. Since the M1 excitation occurs mainly for open-shell nuclei, the nuclear pairing effect is expected to play a role. As expected from the form of operator, this mode may provide the information on the spin-related properties, including the spin component of dineutron and diproton correlations. In general, the sum rule for M1 transition strength has not been derived yet. Purpose: To investigate the M1 excitation of the systems with two valence nucleons above the closed-shell core, with pairing correlation included, and to establish the M1 sum rule that could be used to validate theoretical and experimental approaches. Possibility to utilize the M1 excitation as a tool to investigate the pairing correlation in medium is also discussed. Method: Three-body model, which consists of a rigid spherical core and two valence nucleons, is employed. Interactions for its two-body subsystems are phenomenologically determined in order to reproduce the two-body and three-body energies. We also derive the M1 sum rule within this three-body picture. Conclusion: The introduced M1 sum rule can be utilized as a benchmark for model calculations of M1 transitions in the systems with two valence nucleons. The total sum of the M1 transition strength is related with the coupled spin of valence nucleons in the open shell, where the pairing correlation is unnegligible. The three-body-model calculations for 18 O, 18 Ne, and 42 Ca nuclei demonstrate a significant effect of the pairing correlations on the low-lying M1 transitions. Therefore, further experimental studies of M1 transitions in those systems are on demand, in order to validate proposed sum rule, provide a suitable probe for the nuclear pairing in medium, as well as to optimize the pairing models.Comment: 10 pages, 3 figures, 4 tables. Revised for re-submission to Phys. Rev.