• Korean Journal of Mathematics
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• 제7권2호
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• pp.159-166
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• 1999

For classical elliptic pseudodifferential operators $A({\lambda})$ of order $m$ > 0 with parameter ${\lambda}$ of weight ${\chi}$ > 0, it is known that $logDet_{\theta}A({\lambda})$ admits an asymptotic expansion as ${\theta}{\rightarrow}+{\infty}$. In this paper we show, with some assumptions, that the coefficients of ${\lambda}^-{\frac{n}{\chi}}$ can be expressed by the values of zeta functions at 0 for some elliptic ${\psi}$DO's on $M{\times}S^1{\times}{\cdots}{\times}S^1$ multiplied by $\frac{m}{c_{n-1}}$.