Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bounds for Z$_1$-eigenvalues of generalized Hilbert tensors   In this paper, we introduce the concept of Z$_1$-eigenvalue to infinite
dimensional generalized Hilbert tensors (hypermatrix)
$\mathcal{H}_\lambda^{\infty}=(\mathcal{H}_{i_{1}i_{2}\cdots i_{m}})$,
  $$
  \mathcal{H}_{i_{1}i_{2}\cdots i_{m}}=\frac{1}{i_{1}+i_{2}+\cdots
i_{m}+\lambda},\
  \lambda\in \mathbb{R}\setminus\mathbb{Z}^-;\
i_{1},i_{2},\cdots,i_{m}=0,1,2,\cdots,n,\cdots,
  $$
  and proved that its $Z_1$-spectral radius is not larger than $\pi$ for
$\lambda>\frac{1}{2}$, and is at most $\frac{\pi}{\sin{\lambda\pi}}$ for
$\frac{1}{2}\geq \lambda>0$. Besides, the upper bound of $Z_1$-spectral radius
of an $m$th-order $n$-dimensional generalized Hilbert tensor
$\mathcal{H}_\lambda^n$ is obtained also, and such a bound only depends on $n$
and $\lambda$.

16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph