On the coefficients of the asymptotic of analytic torsion

Abstract

In this article, we study the asymptotic expansion of the analytic torsion associated with positive Hermitian line bundles on projective spaces. We show that the expansion contains no terms of the form $k^{-i}\log k$ for $i\ge 1$. The proof combines the arithmetic Riemann-Roch theorem with an explicit computation of the arithmetic degree of spaces of global sections.