Integral representations of q-analogues of the Hurwitz zeta function

Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at non-positive integers of the q-analogue of the Hurwitz zeta function, and to study the classical limit of this q-analogue. All the discussion developed here is entirely different from the previous work in [4]Comment: 14 page

On Witten multiple zeta-functions associated with semisimple Lie algebras IV

In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types $A_2$, $A_3$, $B_2$, $B_3$ and $C_3$. In this paper, we consider the case of $G_2$-type. We define certain analogues of Bernoulli polynomials of $G_2$-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of $G_2$-type. Next we consider the meromorphic continuation of the zeta-function of $G_2$-type and determine its possible singularities. Finally, by using our previous method, we give explicit functional relations for them which include Witten's volume formulas.Comment: 22 pag

Near-infrared Brightness of the Galilean Satellites Eclipsed in Jovian Shadow: A New Technique to Investigate Jovian Upper Atmosphere

We have discovered that Europa, Ganymede and Callisto are bright around 1.5 {\mu}m even when not directly lit by sunlight, based on observations from the Hubble Space Telescope and the Subaru Telescope. The observations were conducted with non-sidereal tracking on Jupiter outside of the field of view to reduce the stray light subtraction uncertainty due to the close proximity of Jupiter. Their eclipsed luminosity was $10^{-6}$-$10^{-7}$ of their uneclipsed brightness, which is low enough that this phenomenon has been undiscovered until now. In addition, Europa in eclipse was <1/10 of the others at 1.5 {\mu}m, a potential clue to the origin of the source of luminosity. Likewise, Ganymede observations were attempted at 3.6 {\mu}m by the Spitzer Space Telescope but it was not detected, suggesting a significant wavelength dependence. The reason why they are luminous even when in the Jovian shadow is still unknown, but forward-scattered sunlight by haze in the Jovian upper atmosphere is proposed as the most plausible candidate. If this is the case, observations of these Galilean satellites while eclipsed by the Jovian shadow provide us a new technique to investigate Jovian atmospheric composition, and investigating the transmission spectrum of Jupiter by this method is important for investigating the atmosphere of extrasolar giant planets by transit spectroscopy.Comment: 7 pages, 3 figures, accepted to Ap

Are There Nuclear Structure Effects on the Isoscalar Giant Monopole Resonance and Nuclear Incompressibility near A~90?

"Background-free" spectra of inelastic $\alpha$-particle scattering have been measured at a beam energy of 385 MeV in $^{90, 92}$Zr and $^{92}$Mo at extremely forward angles, including 0$^{\circ}$. The ISGMR strength distributions for the three nuclei coincide with each other, establishing clearly that nuclear incompressibility is not influenced by nuclear shell structure near $A\sim$90 as was claimed in recent measurements.Comment: 5 pages, 4 figures; accepted for publication in Phys. Lett.