On the zeta functions on the projective complex spaces

2015/11/13 by Hajli, Mounir
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1511.04375

Abstract

In this article, we study the zeta function ζ_q associated to the Laplace operator Δ_q acting on the space of the smooth (0,q)-forms with q=0,…,n on the complex projective space ℙⁿ(ℂ) endowed with its Fubini-Study metric. In particular, we show that the values of ζ_q at non-positive integers are rational. Moreover, we give a formula for ∑_{q≥ 0}(-1)^q+1qζ_q'(0), the associated holomorphic analytic torsion.

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