Special functions, natural generalizations of the elementary functions (trigonometric, exponential, power fnc. etc.), play an active role in science and engineering not only mathematics. For these functions, various formulas and theorems have been discovered similarly to the trigonometric functions, and furthermore, some beautiful mathematical structures or theories often are hidden in the results. Actually, from the ancient, special functions have been deeply connected with developments of various fields such that differential equations, algebraic geometry, arithmetic, combinatorics, probability, statistics, representation theory and integralble systems etc.
I have studied the following regardless of choice of specific fields or techniques.
1)the Barnes type multiple zeta and gamma functions, which was motivated by some elliptic analogue of special function (in particular, the elliptic gamma functions) .
2)generalized multiple Dedekind sums regarded as a finite analogue of Barnes type multiple zeta functions, and their reciprocity laws, which are associated with periods or multiplier of modular forms.
3)Operator ordering problems of Weyl algebra and Meixner-Pollaczek polynomials
4)Construction and investigation of new multivariate orthogonal polynomials by using an analysis on symmetric cones.
5)A generalization of the Fibonacci and Lucas number from the view point of special values of symmetric functions.
Currently, I am particularly interested in the study of orthogonal functions (polynomials) systems by using unitary transforms. I desire to discover new orthogonal functions and clarify their theoretical background.
- Mar. 2014, Ph.D., Kyushu University
- Apr. 2014, Researcher, Institute of Mathematics for Industry, Kyushu University
- Apr. 2015, Specially Appointed Assistant Professor, Graduate School for Information Science and Technology, Osaka University
- E-mail ： g-shibukawa@ist.
- Tel ： S4565
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