A systematic method for constructing anti-magic squares of every even order (>2) was found. This partially answered an open question asked by Gakuho Abe.

In this paper the normality criterions concerning sharing values are researched and the old Montel theorem and Bloch-Valiron theorem are improved.

In this paper, we study a family of iteration of polynomial map on the 2-dimensional complex Euclidean space {${\bf C}\sp 2$} whose all unbounded orbits converge to one point of the line at infinity in the 2-dimensional complex projective space {${\bf P}\sp 2$}. In particular, we show some sufficient condition for the Lebesgue measure of its Julia set to be equal to 0.

We give explicit formulae in terms of characteristics and intersection multiplicities of branches for the polar quotients of a plane many-branched singularity.

Every flat family of Du Val singularities admits a simultaneous minimal resolution after a finite base change. We investigate a flat family of isolated Gorenstein toric singularities and prove that there exists a simultaneous partial resolution.

We prove that the spinor {$L$}-functions attached to some Siegel cusp forms of degree ≥ 3, which are Ikeda lifts, have meromorphic continuations and the functional equations.