Study of special functions which arise from parametric deformations ofrepresentation-theoretical structures

研究了具有良好的不变性和对称性的行列式的参量变形和量子谐振子。对于行列式的参数化变形，我们利用这种变形得到了一类特殊参数的对称多项式。对于量子谐振子的参量变形，我们证明了描述相关谱zeta函数的某一特殊值的函数满足类似模形式的变换规则。

We have studied a parametric deformation of the determinant and the quantumharmonic oscillator, which are equipped with nice invariance and symmetries. As for the parametric deformation of the determinant, we found certain family of symmetric polynomials by using such deformationsfor special parameters. As for the parametric deformation of the quantum harmonic oscillator, we showedthat the function which describes a certain special value of the associated spectral zeta function satisfiestransformation rules similar to those for modular forms.