Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On two complementary approaches aiming at the definition of the
  determinant of an elliptic partial differential operator   We bring together two apparently disconnected lines of research (of
mathematical and of physical nature, respectively) which aim at the definition,
through the corresponding zeta function, of the determinant of a differential
operator possessing, in general, a complex spectrum. It is shown explicitly how
the two lines have in fact converged to a meeting point at which the precise
mathematical conditions for the definition of the zeta function and the
associated determinant are easy to understand from the considerations coming up
from the physical approach, which proceeds by stepwise generalization starting
from the most simple cases of physical interest. An explicit formula that
establishes the bridge between the two approaches is obtained.

31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
9
The categories of this paper are: nlin