IJPAM: Volume 26, No. 3 (2006)

ON THE LOGARITHMIC DERIVATIVE OF
THE $\zeta$-DETERMINANT

Oscar A. Barraza
Department of Mathematics
Faculty of Exact Sciences
National University of La Plata
La Plata, C.C. 172, 1900, ARGENTINA
e-mail: oscar@mate.unlp.edu.ar


Abstract.A formula for the derivative of the logarithm of the $\zeta$-determinant of the quotient of two elliptic pseudodifferential operators, acting between the fibers of a vector bundle over a $n$-dimensional closed manifold $M$, is presented in this article. Although this formula is not unknown, the hypotheses are relaxed in the version given here.

Received: December 21, 2005

AMS Subject Classification: 58J52, 58J32, 58J40

Key Words and Phrases: $\zeta$-determinant, Fredholm determinant, trace class, pseudodifferential operator theory

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 3