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Tsuyoshi Miezaki

  1. On Euclidean designs and the potential energy.

    Втр, 09/13/2011 - 15:01 — SomNambul
    Authors: Tsuyoshi Miezaki, Makoto Tagami
    Subjects: Combinatorics
    Abstract

    We study Euclidean designs from the viewpoint of the potential energy. For a
    finite set in Euclidean space, We formulate a linear programming bound for the
    potential energy by applying harmonic analysis on a sphere. We also introduce
    the concept of strong Euclidean designs from the viewpoint of the linear
    programming bound, and we give a Fisher type inequality for strong Euclidean
    designs. A finite set on Euclidean space is called a Euclidean a-code if any
    distinct two points in the set are separated at least by a.

  2. Toy models for D. H. Lehmer's conjecture II.

    Пнд, 04/12/2010 - 15:01 — SomNambul
    Authors: Tsuyoshi Miezaki, Eiichi Bannai
    Subjects: Number Theory
    Abstract

    In the previous paper, we studied the "Toy models for D. H. Lehmer's
    conjecture". Namely, we showed that the m-th Fourier coefficient of the
    weighted theta series of the $\mathbb{Z}^2$-lattice and the $A_{2}$-lattice
    does not vanish, when the shell of norm $m$ of those lattices is not the empty
    set. In other words, the spherical 4 (resp. 6)-design does not exist among the
    nonempty shells in the $\mathbb{Z}^2$-lattice (resp. $A_{2}$-lattice). This
    paper is the sequel to the previous paper.

  3. On a property of 2-dimensional integral Euclidean lattices.

    Чт, 12/10/2009 - 16:01 — SomNambul
    Authors: Tsuyoshi Miezaki, Eiichi Bannai
    Subjects: Combinatorics
    Abstract

    Let $L$ be any integral lattice in the 2-dimensional Euclidean space.
    Generalizing the earlier works of Hiroshi Maehara and others, we prove that for
    every integer $n>0$, there is a circle in the plane $\mathbb{R}^{2}$ that
    passes through exactly $n$ points of $L$.

  4. Nonexistence for extremal Type II $\ZZ_{2k}$-Codes.

    Втр, 08/25/2009 - 22:41 — SomNambul
    Authors: Tsuyoshi Miezaki
    Subjects: Combinatorics
    Abstract

    In this paper, we show that an extremal Type II $\ZZ_{2k}$-code of length $n$
    dose not exist for all sufficiently large $n$ when $k=2,3,4,5,6$.

Math-arch

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