121 research outputs found

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

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    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, CFHD=LHD/Lbol\rm CF_{HD} = {\it L}_{HD} / {\it L}_{bol}, where the LHD{L}_{\rm HD} is the luminosity from the hot dust component and the Lbol{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 zz\sim0.3 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 \sim10 times higher than unobscured type 1 quasars, suggesting a heavy dust extinction with AV>2.5A_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 CFHD\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 353 \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

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    We prove the transfer congruence between pp-adic Hecke LL-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 qq-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 LL-function of a CM elliptic curve twisted by Artin representations. As a second application, we prove the existence of a non-commutative pp-adic LL-function in the algebraic K1K_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

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    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

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    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

    TRC: Trust Region Conditional Value at Risk for Safe Reinforcement Learning

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    As safety is of paramount importance in robotics, reinforcement learning that reflects safety, called safe RL, has been studied extensively. In safe RL, we aim to find a policy which maximizes the desired return while satisfying the defined safety constraints. There are various types of constraints, among which constraints on conditional value at risk (CVaR) effectively lower the probability of failures caused by high costs since CVaR is a conditional expectation obtained above a certain percentile. In this paper, we propose a trust region-based safe RL method with CVaR constraints, called TRC. We first derive the upper bound on CVaR and then approximate the upper bound in a differentiable form in a trust region. Using this approximation, a subproblem to get policy gradients is formulated, and policies are trained by iteratively solving the subproblem. TRC is evaluated through safe navigation tasks in simulations with various robots and a sim-to-real environment with a Jackal robot from Clearpath. Compared to other safe RL methods, the performance is improved by 1.93 times while the constraints are satisfied in all experiments.Comment: RA-L and ICRA 202

    Abelian arithmetic Chern-Simons theory and arithmetic linking numbers

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    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
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