Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determinant of Laplacians on Heisenberg Manifolds   We give an integral representaion of the zeta-reguralized determinant of
Laplacians on three dimensional Heisenberg manifolds, and study a behaivior of
the values when we deform the uniform discrete subgroups. Heiseberg manifolds
are the total space of a fiber bundle with a torus as the base space and a
circle as a typical fiber, then the deformation of the uniform discrete
subgroups means that the "radius" of the fiber goes to zero. We explain the
lines of the calculations precisely for three dimensional cases and state the
corresponding results for five dimensional Heisenberg manifolds. We see that
the values themselves are of the product form with a factor which is that of
the flat torus. So in the last half of this paper we derive general formulas of
the zeta-regularized determinant for product type manifolds of two Riemannian
manifolds, discuss the formulas for flat tori and explain a relation of the
formula for the two dimensional flat torus and Kronecker's second limit
formula.

7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin