1,710 research outputs found

    On the special values of certain L-series related to half-integral weight modular forms

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    Let h be a cuspidal Hecke eigenform of half-integral weight, and En/2+1/2 be Cohen’s Eisenstein series of weight n/2+1/2. For a Dirichlet character χ we define a certain linear combination R(χ)(s, h,En/+1/2) of the Rankin-Selberg convolution products of h and En/2+1/2 twisted by Dirichlet characters related with χ. We then prove a certain algebraicity result for R(χ)(l, h,En/2+1/2) with l integers

    X-ray scattering from crystalline SiO2 in the thermal oxide layers on vicinal Si(111) surfaces

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    Shimura, T., Misaki, H. & Umeno, M. (1996). Acta Cryst. A52, C465, https://doi.org/10.1107/S0108767396080932

    Interacting quantum rotors in oxygen-doped germanium

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    We investigate the interaction effect between oxygen impurities in crystalline germanium on the basis of a quantum rotor model. The dipolar interaction of nearby oxygen impurities engenders non-trivial low-lying excitations, giving rise to anomalous behaviors for oxygen-doped germanium (Ge:O) below a few degrees Kelvin. In particular, it is theoretically predicted that Ge:O samples with oxygen-concentration of 101718^{17-18}cm3^{-3} show (i) power-law specific heats below 0.1 K, and (ii) a peculiar hump in dielectric susceptibilities around 1 K. We present an interpretation for the power-law specific heats, which is based on the picture of local double-well potentials randomly distributed in Ge:O samples.Comment: 13 pages, 11 figures; to be published in Phys. Rev.
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