Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tight universal quadratic forms   For a positive integer $n$, let $\mathcal T(n)$ be the set of all integers
greater than or equal to $n$. An integral quadratic form $f$ is called tight
$\mathcal T(n)$-universal if the set of nonzero integers that are represented
by $f$ is exactly $\mathcal T(n)$. The smallest possible rank over all tight
$\mathcal T(n)$-universal quadratic forms is defined by $t(n)$. In this
article, we find all tight $\mathcal T(n)$-universal diagonal quadratic forms.
We also prove that $t(n) \in \Omega(\log_2(n)) \cap O(\sqrt{n})$. Explicit
lower and upper bounds for $t(n)$ will be provided for some small integer $n$.

28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin