# IJPAM: Volume 26, No. 3 (2006)

ON THE LOGARITHMIC DERIVATIVE OF
THE -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 -determinant of the quotient of two elliptic pseudodifferential operators, acting between the fibers of a vector bundle over a -dimensional closed manifold , is presented in this article. Although this formula is not unknown, the hypotheses are relaxed in the version given here.