Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heat coefficients for magnetic Laplacians on the complex projective
  space $\mathbf{P}^{n}(\mathbb{C})$   Denoting by $\Delta_\nu$ the Fubini-Study Laplacian perturbed by a uniform
magnetic field strength proportional to $\nu$, this operator has a discrete
spectrum consisting on eigenvalues $\beta_m, \ m\in\mathbb{Z}_+$, when acting
on bounded functions of the complex projective $n$-space. For the corresponding
eigenspaces, we give a new proof for their reproducing kernels by using
Zaremba's expansion directly. These kernels are then used to obtain an integral
representation for the heat kernel of $\Delta_\nu$. Using a suitable polynomial
decomposition of the multiplicity of each $\beta_m$, we write down a trace
formula for the heat operator associated with $\Delta_\nu$ in terms of Jacobi's
theta functions and their higher order derivatives. Doing so enables us to
establish the asymptotics of this trace as $t\searrow 0^+$ by giving the
corresponding heat coefficients in terms of Bernoulli numbers and polynomials.
The obtained results can be exploited in the analysis of the spectral zeta
function associated with $\Delta_\nu$.

33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org