We show that the modular functions j 1,5 and j 1,6 generate function fields of the modular curves X 1 (N) (N = 5, 6, respectively) and find some number-theoretic properties of these modular functions.
BACKGROUND/AIMS Pre-existing diabetes mellitus (DM) has been identified as an adverse prognostic variable associated with increased mortality in various cancers. Although DM and hyperglycemia are considered risk factors for pancreatic cancer (PC), antidiabetic treatments for patients with advanced PC have been overlooked. This study aimed to evaluate the… (More)
BACKGROUND/AIMS The modification of the Model for End-Stage Liver Disease (MELD) scoring system (Refit MELD) and the modification of MELD-Na (Refit MELDNa), which optimized the MELD coefficients, were published in 2011. We aimed to validate the superiority of the Refit MELDNa over the Refit MELD for the prediction of 3-month mortality in Korean patients… (More)
Let k be an imaginary quadratic field, h the complex upper half plane, and let τ ∈ h ∩ k, q = e πiτ. In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in  and  by using Berndt's idea (). Using this, we get special transcendental numbers. For example, q 1/8 1 + −q 1+q + −q 2… (More)
We find the super-replication formulae which would be a generalization of replication formulae. And we apply the formulae to derive periodically vanishing property in the Fourier coefficients of the Hauptmodul N (j 1,12) as a super-replicable function.
BACKGROUND/AIMS A revised classification system for renal dysfunction in patients with cirrhosis was proposed by the Acute Dialysis Quality Initiative and the International Ascites Club Working Group in 2011. The aim of this study was to determine the prevalence of renal dysfunction according to the criteria in this proposal. METHODS The medical records… (More)
Let K be an imaginary quadratic field. We show by adopting Schertz's argument with the Siegel-Ramachandra invariant() that singular values of certain quotients of the ∆-function generate ring class fields over K(Theorems 4.2, 5.4 and Remark 5.5).
We extend Norton-Borcherds-Koike's replication formulae to super-replicable ones by working with the congruence groups Γ 1 (N) and find the product identities which characterize super-replicable functions. These will provide a clue for constructing certain new infinite dimensional Lie superalgebras whose denominator identities coincide with the above… (More)