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

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

Interacting quantum rotors in oxygen-doped germanium

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 10$^{17-18}$cm$^{-3}$ 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.

CeCu_2Ge_2: Challenging our Understanding of Quantum Criticality

Here, we unveil evidence for a quantum phase-transition in CeCu_2Ge_2 which displays both an incommensurate spin-density wave (SDW) ground-state, and a strong renormalization of the quasiparticle effective masses (mu) due to the Kondo-effect. For all angles theta between an external magnetic field (H) and the crystallographic c-axis, the application of H leads to the suppression of the SDW-state through a 2^nd-order phase-transition at a theta-dependent critical-field H_p(theta) leading to the observation of small Fermi surfaces (FSs) in the paramagnetic (PM) state. For H || c-axis, these FSs are characterized by light mu's pointing also to the suppression of the Kondo-effect at H_p with surprisingly, no experimental evidence for quantum-criticality (QC). But as $H$ is rotated towards the a-axis, these mu's increase considerably becoming undetectable for \theta > 56^0 between H and the c-axis. Around H_p^a~ 30 T the resistivity becomes proportional T which, coupled to the divergence of mu, indicates the existence of a field-induced QC-point at H_p^a(T=0 K). This observation, suggesting FS hot-spots associated with the SDW nesting-vector, is at odds with current QC scenarios for which the continuous suppression of all relevant energy scales at H_p(theta,T) should lead to a line of quantum-critical points in the H-theta plane. Finally, we show that the complexity of its magnetic phase-diagram(s) makes CeCu_2Ge_2 an ideal system to explore field-induced quantum tricritical and QC end-points.Comment: 10 pages, 5 figures, Phys. Rev. B (in press

Restricted sum formula of alternating Euler sums

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Crystal structure, electronic, and magnetic properties of the bilayered rhodium oxide Sr3Rh2O7

The bilayered rhodium oxide Sr3Rh2O7 was synthesized by high-pressure and high-temperature heating techniques. The single-phase polycrystalline sample of Sr3Rh2O7 was characterized by measurements of magnetic susceptibility, electrical resistivity, specific heat, and thermopower. The structural characteristics were investigated by powder neutron diffraction study. The rhodium oxide Sr3Rh2O7 [Bbcb, a = 5.4744(8) A, b = 5.4716(9) A, c = 20.875(2) A] is isostructural to the metamagnetic metal Sr3Ru2O7, with five 4d electrons per Rh, which is electronically equivalent to the hypothetic bilayered ruthenium oxide, where one electron per Ru is doped into the Ru-327 unit. The present data show the rhodium oxide Sr3Rh2O7 to be metallic with enhanced paramagnetism, similar to Sr3Ru2O7. However, neither manifest contributions from spin fluctuations nor any traces of a metamagnetic transition were found within the studied range from 2 K to 390 K below 70 kOe.Comment: To be published in PR