Researcher Information

Keiji Matsumoto


Discovery of formulae of special functions

Department of Mathematics, Mathematics


Study of special functions admitting integral representations by twisted (co)homology groups

FieldSpecial functions
KeywordSpecial functions, Theta functions, Hypergeometric functions, Twisted (co)homology groups

Introduction of Research

There are many special functions defined by integrals or admitting integral representations such as the gamma functions, the beta function, the zeta function and the hypergeometric function. I study these functions geometrically by regarding integrals as pairings of some kinds of homology groups and that of cohomology groups. I also attempt to find modular functions and modular forms by considering period maps for families of algebraic varieties as generalizations of a fact that the elliptic modular function appears as the inverse of the period map for the family of elliptic curves.

Academic degreeDoctor of Science
Affiliated academic societyThe Mathematical Society of Japan
Room addressFaculty of ScienceBuilding No.4 4-407