118 research outputs found

### 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 $p$-adic Hecke $L$-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

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

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

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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