Ray class fields generated by torsion points of certain elliptic curves

We first normalize the derivative Weierstrass $\wp'$-function appearing in Weierstrass equations which give rise to analytic parametrizations of elliptic curves by the Dedekind $\eta$-function. And, by making use of this normalization of $\wp'$ we associate certain elliptic curve to a given imaginary quadratic field $K$ and then generate an infinite family of ray class fields over $K$ by adjoining to $K$ torsion points of such elliptic curve. We further construct some ray class invariants of imaginary quadratic fields by utilizing singular values of the normalization of $\wp'$, as the $y$-coordinate in the Weierstrass equation of this elliptic curve, which would be a partial result for the Lang-Schertz conjecture of constructing ray class fields over $K$ by means of the Siegel-Ramachandra invariant

Gauss' form class groups and Shimura's canonical models

Let $N$ be a positive integer and $\Gamma$ be a subgroup of $\mathrm{SL}_2(\mathbb{Z})$ containing $\Gamma_1(N)$. Let $K$ be an imaginary quadratic field and $\mathcal{O}$ be an order of discriminant $D_\mathcal{O}$ in $K$. Under some assumptions, we show that $\Gamma$ induces a form class group of discriminant $D_\mathcal{O}$ (or, of order $\mathcal{O}$) and level $N$ if and only if there is a certain canonical model of the modular curve for $\Gamma$ defined over a suitably small number field. In this way we can find an interesting link between two different subjects.Comment: 18 page

Remifentanil Prevents Withdrawal Movements Caused by Intravenous Injection of Rocuronium

PURPOSE: The incidence of pain induced withdrawal movement following intravenous injection of rocuronium is high. This randomized, double-blind, placebo-controlled study was designed to evaluate the effect of pretreatment of remifentanil on the withdrawal movements due to intravenous injection of rocuronium during anesthetic induction. MATERIALS AND METHODS: Ninety adult female patients undergoing thyroidectomy were randomly allocated to three groups. Each patient intravenously received one of three solutions of equal volume (4 mL): normal saline (Group I, n=30), 0.5 microg/kg remifentanil (Group II, n=30) or 1 microg/kg remifentanil (Group III, n=30). Thirty seconds after remifentanil administration, anesthesia was induced with 5 mg/kg IV thiopental. Twenty seconds after thiopental injection, 0.6 mg/kg IV rocuronium was administered (injection rate of 0.5 mL/sec) and patients' withdrawal movements were assessed. Mean arterial pressure (MAP) and heart rate were assessed on arrival in the operation room, before the tracheal intubation and immediately, 1 and 2 min after the tracheal intubation. RESULTS: The incidence of withdrawal movements was significantly lower in both of the remifentanil groups (3 and 0% in Group II and III, respectively) than in the saline group (70%). Remifentanil attenuated the increase of heart rate and MAP immediately and 1 min after the tracheal intubation. CONCLUSION: The pretreatment with 0.5 and 1.0 microg/kg remifentanil of bolus doses prevented the withdrawal movements caused by rocuronium injection, and effectively blunted cardiovascular activation following tracheal intubationope

Arithmetic properties of orders in imaginary quadratic fields

Let $K$ be an imaginary quadratic field. For an order $\mathcal{O}$ in $K$ and a positive integer $N$, let $K_{\mathcal{O},\,N}$ be the ray class field of $\mathcal{O}$ modulo $N\mathcal{O}$. We deal with various subjects related to $K_{\mathcal{O},\,N}$, mainly about Galois representations attached to elliptic curves with complex multiplication, form class groups and $L$-functions for orders

Observation of photon-pair generation in the normal group-velocity-dispersion regime with slight detuning from the pump wavelength

A fiber-based photon-pair source in the telecom C-band is suitable for quantum information science including quantum communications. Spontaneous four-wave mixing effects are known to create photon pairs that are slightly detuned from the pump wavelength only in the anomalous group-velocity-dispersion (GVD) regime. Here, we achieve high-quality photon-pair generation slightly detuned from the pump wavelength in the normal GVD regime through a dispersion shifted fiber, for the first time. The photon pairs in C-band exhibit strong temporal correlation with each other and excellent heralded anti-bunching property. This photon-pair generation scheme can be exploited as telecom-band quantum light sources for quantum information applications.11Ysciescopu

Class fields arising from the form class groups of order O and level N

Let $K$ be an imaginary quadratic field and $\mathcal{O}$ be an order in $K$. We construct class fields associated with form class groups which are isomorphic to certain $\mathcal{O}$-ideal class groups in terms of the theory of canonical models due to Shimura. By utilizing these form class groups, we first derive a congruence relation on special values of a modular function of higher level as an analogue of Kronecker's congruence relation. Furthermore, as an application of such class fields, for a positive integer $n$ we examine primes of the form $x^2+ny^2$ with some additional conditions.Comment: 30 page