Eiichi Bannai, Etsuko Bannai and Junichi Shigezumi

Ann. Comb. 16(4) 651-659 Dec 2012 [Refereed]

Euclidean -designs, which are finite weighted subsets of Euclidean space, were defined by Neumaier-Seidel (1988). A tight -design is defined as a -design whose cardinality is equal to the known natural lower bound.

Discrete Mathematics 312(22) 3283-3292 Nov 2012 [Refereed]

We classify the maximal m-distance sets in which contain the representation of
the Johnson graph for . Furthermore, we determine the necessary and
sufficient condition for and such that the representa...

We determine the location of all of the zeros of certain Poincaré series associated with the Fricke groups and in their fundamental domains by applying and extending the method of F.K.C. Rankin and H.P.F. Swinne...

Asian-European Journal of Mathematics 2(2) 239-253 Jun 2009 [Refereed]

A set of vectors all of which have a constant (non-zero) norm value in an Euclidean lattice is called a shell of the lattice. Venkov classified strongly perfect lattices of minimum (Réseaux et ``designs'' sphérique, 2001), whose minima...

Maruhashi, K.; Shigezumi, J.; Yugami, N.; Faloutsos, C.

Data Mining Workshops (ICDMW), 2012 IEEE 12th International Conference on 234-241 Dec 2012 [Refereed]

Estimating the distances of the shortest path between given pairs of nodes in a graph is a basic operation in a wide variety of applications including social network analysis, web retrieval, etc. Such applications require a response on the order o...

[[Part I]]: On the zeros of certain modular functions [Ch. 1]: On the zeros of Eisenstein series for and [Ch. 2]: On the zeros of Eisenstein series for and [Ch. 3]: On the zeros of ce...

Mini-Workshop "Algebraic Combinatorics" (Japanese) Mar 2010

We introduce a new example of Euclidean tight 6-design of supported by two concentric spheres. Let the design be split as , and . Then each is a spherical 4-design, and is tight....

Mini-Workshop on Algebra and Combinatorics 2009 Aug 2009 Junichi Shigezumi, Katsuhiko Ono

Let be a prime, and we consider supersingular elliptic curves over a field of characteristic . Then, the polynomial , every root of which is -invariant of some supersingular elliptic curve, is called a {\it supersingular ...

Certain classifications of lattices and spherical designs

Junichi Shigezumi

The 1st Kumjung Seminar Feb 2009

A lattice, whose minimal shell is a spherical 5-design, is said to be strongly perfect. B. B. Venkov classified strongly perfect lattices of minimum 3. We talk about the classification of integral lattices whose shells of norm 3 are 5-designs.

We...

On the zeros of Eisenstein series for Fuchsian groups of first kind

Junichi Shigezumi

2nd Japanese-German Number Theory Workshop Feb 2008

We talk about the location of the zeros of the Eisenstein series of one variable which is associated with genus zero Fuchsian groups of the first kind having 1 as a cusp. We introduce small generalization of the result of Professor Heekyoung Hahn,...

On the zeros of Eisenstein series associated with and

Tsuyoshi Miezaki, Hiroshi Nozaki, and Junichi Shigezumi

The Second COE Workshop on Sphere Packing Jun 2005