On a polynomial zeta function

Abstract

We introduce a polynomial zeta function ${\zeta }_{P_n}^{(p)}$, related to certain problems of mathematical physics, and compute its value and the value of its first derivative at the origin $s=0$, by means of a very simple technique. As an application, we compute the determinant of the Dirac operator on quaternionic vector spaces.

7 pages, 1 figure

References in corpus (2)

• Spectral analysis and zeta determinant on the deformed spheres
• Zeta determinant for double sequences of spectral type