Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hessian of the zeta function for the Laplacian on forms   Let M be a compact closed n-dimensional manifold. Given a Riemannian metric
on M, we consider the zeta function Z(s) for the de Rham Laplacian and the
Bochner Laplacian on p-forms. The hessian of Z(s) with respect to variations of
the metric is given by a pseudodifferential operator T(s). When the real part
of s is less than n/2-1, we compute the principal symbol of T(s). This can be
used to determine whether the general critical metric for Z(s) or one of its s
derivatives has finite index, or whether it is an essential saddle point.

19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci