Hitoshi Nakada

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In a recent paper, the first and third author proved a central limit theorem for the number of coprime solutions of the diophantine approximation problem for formal Laurent series in the setting of the classical theorem of Khintchine. In this note, we consider a more general setting and show that even an invariance principle holds, thereby improving upon(More)
We consider metric results for the asymptotic behavior of the number of solutions of Diophantine approximation inequalities with restricted denominators for Laurent formal power series with coefficients in a finite field. We especially consider approximations by rational functions whose denominators are powers of irreducible polynomials, and study the(More)
Abstract The purpose of this paper is to describe the relation between the Legendre and the Lenstra constants. Indeed we show that they are equal whenever the Legendre constant exists; in particular, this holds for both Rosen continued fractions and α-continued fractions. We also give the explicit value of the entropy of the Rosen map with respect to the(More)
Energy levels and electromagnetic properties of 24 nuclides with N = 28 ∼ 30 are studied in terms of a large-scale shell model calculation, which contains no newly adjusted parameters. The Kuo-Brown G-matrix interaction is shown to reproduce energy levels of 205 low-lying states of all these nuclei. We evaluate effective charges by incorporating the(More)
This paper studies digit-cost functions for the Euclid algorithm on polynomials with coefficients in a finite field, in terms of the number of operations performed on the finite field Fq . The usual bit-complexity is defined with respect to the degree of the quotients; we focus here on a notion of ‘fine’ complexity (and on associated costs) which relies on(More)
We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of “symmetric measure”: exchangeability and the Gibbs (or conformal) property. We show that equilibrium measures for such shifts (unique and weak Bernoulli in the one dimensional case) exhibit a variety of spectral properties.
We discuss the mirror asymmetry in light sd-shell nuclei by using recent data on nuclei near the proton drip line. It is clarified that the many-body effects are as important as the single-particle effects. The reduction in the amount of residual interaction matrix elements concerning the (1s1/2)p orbit plays a significant role in the Thomas-Ehrman shifts.(More)