What makes red quasars red? Observational evidence for dust extinction from line ratio analysis

Red quasars are very red in the optical through near-infrared (NIR) wavelengths, which is possibly due to dust extinction in their host galaxies as expected in a scenario in which red quasars are an intermediate population between merger-driven star-forming galaxies and unobscured type 1 quasars. However, alternative mechanisms also exist to explain their red colors: (i) an intrinsically red continuum; (ii) an unusual high covering factor of the hot dust component, that is, $\rm CF_{HD} = {\it L}_{HD} / {\it L}_{bol}$, where the ${L}_{\rm HD}$ is the luminosity from the hot dust component and the ${L}_{\rm bol}$ is the bolometric luminosity; and (iii) a moderate viewing angle. In order to investigate why red quasars are red, we studied optical and NIR spectra of 20 red quasars at $z\sim$0.3 and 0.7, where the usage of the NIR spectra allowed us to look into red quasar properties in ways that are little affected by dust extinction. The Paschen to Balmer line ratios were derived for 13 red quasars and the values were found to be $\sim$10 times higher than unobscured type 1 quasars, suggesting a heavy dust extinction with $A_V > 2.5$ mag. Furthermore, the Paschen to Balmer line ratios of red quasars are difficult to explain with plausible physical conditions without adopting the concept of the dust extinction. The $\rm CF_{HD}$ of red quasars are similar to, or marginally higher than, those of unobscured type 1 quasars. The Eddington ratios, computed for 19 out of 20 red quasars, are higher than those of unobscured type 1 quasars (by factors of $3 \sim 5$), and hence the moderate viewing angle scenario is disfavored. Consequently, these results strongly suggest the dust extinction that is connected to an enhanced nuclear activity as the origin of the red color of red quasars, which is consistent with the merger-driven quasar evolution scenario.Comment: 14 pages, 13 figures, Accepted for publication in A&

On the transfer congruence between pp-adic Hecke LL-functions

We prove the transfer congruence between $p$-adic Hecke $L$-functions for CM fields over cyclotomic extensions, which is a non-abelian generalization of the Kummer's congruence. The ingredients of the proof include the comparison between Hilbert modular varieties, the $q$-expansion principle, and some modification of Hsieh's Whittaker model for Katz' Eisenstein series. As a first application, we prove explicit congruence between special values of Hasse-Weil $L$-function of a CM elliptic curve twisted by Artin representations. As a second application, we prove the existence of a non-commutative $p$-adic $L$-function in the algebraic $K_1$-group of the completed localized Iwasawa algebra.Comment: 59 page

AN APPLICATION OF LAZARD’S THEORY OF p-ADIC LIE GROUPS TO TORSION SELMER POINTED SETS

We construct torsion Selmer pointed sets, which are a discrete analogue of Selmer schemes. Such torsion objects were first defined by K. Sakugawa under a hypothesis, who also established a control theorem for them. We remove the hypothesis and provide the discrete analogue in full generality, to which Sakugawa’s control theorem extends as well. As a key ingredient, we use Lazard’s theory to build the unipotent completion of a finitely generated group over p-adic integers

The proportion of monogenic orders of prime power indices of the pure cubic field

In this paper, we investigate the proportion of monogenic orders among the orders whose indices are a power of a fixed prime in a pure cubic field. We prove that the proportion is zero for a prime number that is not equal to 2 or 3. To do this, we first count the number of orders whose indices are power of a fixed prime. This is done by considering every full rank submodules of the ring of integers, and establishing the condition to be closed under multiplication. Next, we derive the index form of arbitrary orders based on the index form of the ring of integers. Then, we obtain an upper bound of the number of monogenic orders with prime power indices by applying the finiteness of the number of primitive solutions of the Thue-Mahler equation

Abelian arithmetic Chern-Simons theory and arithmetic linking numbers

Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to a precise arithmetic analogue of a 'path-integral formula' for linking numbers

Strategy for determining vaccination user fees and locations: a case study in rural China

Despite the enormous success of vaccinations in decreasing disease burden, there are still millions of deaths from vaccine-preventable diseases worldwide, especially in the developing world. The literature reports that people living in rural areas in China often fail to be immunized not only because of inability to pay user fee but also due to poor geographical accessibility to vaccination sites. However, the level of user fees and the locations of vaccination sites have not been systematically determined in vaccination planning practices, and little research effort has been dedicated to develop a scientific tool to design optimal vaccination strategies. This dissertation addresses important policy questions of how many vaccination sites are needed, where they should be located, and how much users should be charged, so as to maximize the outcomes of vaccination programs under budget constraints. This research develops a decision-analytic tool to address these policy questions based on optimization models integrated with various quantitative techniques. The data were collected from a case study conducted in a rural area of southern China in 2004 with contingent valuation (CV) surveys to assess households’ willingness to pay for typhoid vaccinations and using geographical information systems (GIS) to obtain location and road information. The data were used to estimate a household demand function for vaccinations which depends on user travel distance as well as the user fee. Using the demand information in location models and simulations, this research demonstrates how the outcomes of vaccination programs change based upon the outpost locations and user fees, along with evidence of substantial private benefits brought about by locating outposts closer to users. It also estimates a cost function to show how much of the costs of delivering vaccinations are associated with the number of outposts and the range of vaccination coverage. All these results are integrated into an optimization tool to seek out the user fee and locations of vaccination outposts that meets specific policy objectives. Upon successful adoption and implementation in actual planning processes, this tool could play a critical role in determining user fees and locations for market-based public health vaccination services in developing countries