Xin-qi Luo

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20232026

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math.NT2024

On certain determinants and the square root of some determinants involving Legendre Symbols

Chen-kai Ren, Xin-qi Luo

Let $p > 3$ be a prime and $(\frac{.}{p})$ be the Legendre symbol. For any integer $d$ with $p ∤ d$ and any positive integer $m$ , Sun introduced the determinants $$T_m(d,p)=\det\l…

math.NT2024

Legendre symbols related to $D_{p} (b, 1)$

Xin-Qi Luo, Wei Xia

Let $p$ be an odd prime. For any $b, c \in Z$ , Z.-W. Sun introduced the new-type determinant $D_{p} (b, c) = ∣ (i^{2} + bij + c j^{2})^{p - 2} ∣_{1 ⩽ i, j ⩽ p - 1},$ and studied it…

math.NT2023

On the natural density of integers $n$ for which $σ (k n + r_{1}) > σ (k n + r_{2})$

Xin-qi Luo, Chen-kai Ren

For any positive integer $n$ , let $σ (n) = \sum_{d ∣ n} d$ . In 2020, M. Kobayashi and T. Trudgian showed that the natural density of positive integers n with $σ(kn+r_1) \geq σ(kn+r_…

On certain determinants and the square root of some determinants involving Legendre Symbols

Legendre symbols related to Dp​(b,1)

On the natural density of integers n for which σ(kn+r1​)>σ(kn+r2​)

Legendre symbols related to $D_{p} (b, 1)$

On the natural density of integers $n$ for which $σ (k n + r_{1}) > σ (k n + r_{2})$