Research Field
Department of Mathematics
Research Interest
Special Functions
Research Activities

There are many special functions defined by integrals or admitting integral representations, such as the gamma function, the beta function, the zeta function, and the hypergeometric function.
We regard these integrals as pairings between elements of some kinds of homology groups and those of cohomology groups. From this point of view, I attempt to find formulas for special functions and to give them geometrical meanings. On the other hand, it is classically known that the elliptic modular function appears as the inverse of the period map for a family of elliptic curves. I study modular forms and modular functions on bounded symmetric domains by the inverses of period maps of families of algebraic varieties.

1. Matsumoto, Keiji;
Theta functions on the bounded symmetric domain of type $I_{2,2}$
and the period map of a 4-parameter family of K3 surfaces.
Math. Ann. 295 (1993), no. 3, 383–409.

2. Matsumoto, Keiji and Terasoma, Tomohide;
Arithmetic-geometric means for hyperelliptic curves and Calabi-Yau varieties.
Internat. J. Math. 21 (2010), no. 7, 939–949.

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