Xue-Jun Guo

activity

20232026

collaborators

10 papers

math.NT2026

On the Fractional Parts of Polynomials Modulo $p$

Xuejun Guo, Chen Lin, Zhefeng Xu

We study a half-interval distribution problem for polynomial residues modulo an odd prime $p$ : how often the fractional part of $φ (x) / p$ lies in the upper half of the unit interval…

math.NT2026

The $p$ -rationality of $Q (- (k p + m))$ and $Q (p (p + 1))$

Chen Lin, Xuejun Guo

In this paper, we construct new families of imaginary and real quadratic fields that are $p$ -rational. In the imaginary case, we prove that for any positive integer $k$ and any int…

math.NT2026

Signs of Square-Free Fourier Coefficients of Half-Integral weight cusp forms and the Congruent Number Problem

Wei Tao, Guo Xuejun

We study the sign distribution of square-free Fourier coefficients of half-integral weight cusp forms. We prove that, for half-integral weight cusp forms $f$ satisfying the eigen…

math.NT2026

Matrix Kloosterman sums and product-trace estimates for semisimple algebras

Xuejun Guo, Chen Lin, Chenhao Tang

Let $k = F_{q}$ , $E = F_{q^{n}}$ and $Tr = Tr_{E / k}$ . For $r \geq 2$ , $a \in k^{\times}$ and $x \in E^{\times}$ , let $N (E, r, x, a)$ be the number of $r…

math.NT2026

Inequalities for $ζ (s) - ψ (1 - s)$ related to a conjecture of Henry

Liwen Gao, Xuejun Guo

In this paper we investigate analytic inequalities related to a conjecture of Henry involving the difference between the Riemann zeta function and the digamma function. By treating…

math.NT2025

Integrality of a trigonometric determinant arising from a conjecture of Sun

Liwen Gao, Xuejun Guo

In this paper we resolve a conjecture of Zhi-Wei Sun concerning the integrality and arithmetic structure of certain trigonometric determinants. Our approach builds on techniques de…

math.NT2025

Trigonometric Determinants via special values of Dirichlet $L$ -Functions

Liwen Gao, Xuejun Guo

In this paper, we investigate the determinants involving some trigonometric functions. We establish a connection between these determinants and the special values of Dirichlet L-fu…

math.NT2025

Central $L$ values of congruent number elliptic curves

Xuejun Guo, Dongxi Ye, Hongbo Yin

Let $E_{n}$ be the congruent number elliptic curve $y^{2} = x^{3} - n^{2} x$ , where $n$ is square-free and not divisible by primes $p \equiv 3 (mod 4)$ . In this paper, we prove that $L (E_{n}, 1)$ ca…

math.NT2024

The asymptotic estimation of prime ideals in imaginary quadratic fields and Chebyshev's bias

Chen Lin, Chenhao Tang, Xuejun Guo

We study the asymptotic estimation of prime ideals that satisfy certain congruence and argument conditions in imaginary quadratic fields. We also discuss the phenomenon of Chebyshe…

math.SP2023

A new approach for constructing graph being determined by their generalized $Q$ -spectrum

Liwen Gao, Xuejun Guo

Given a graph $G$ , we have the adjacency matrix $A (G)$ and degree diagonal matrix $D (G)$ . The $Q$ -spectrum is the all eigenvalues of $Q$ -matrix $Q (G) = A (G) + D (G)$ . A class of graphs…

On the Fractional Parts of Polynomials Modulo p

The p-rationality of Q(−(kp+m)​) and Q(p(p+1)​)

Signs of Square-Free Fourier Coefficients of Half-Integral weight cusp forms and the Congruent Number Problem

Matrix Kloosterman sums and product-trace estimates for semisimple algebras

Inequalities for ζ(s)−ψ(1−s) related to a conjecture of Henry

Integrality of a trigonometric determinant arising from a conjecture of Sun

Trigonometric Determinants via special values of Dirichlet L-Functions

Central L values of congruent number elliptic curves

The asymptotic estimation of prime ideals in imaginary quadratic fields and Chebyshev's bias

A new approach for constructing graph being determined by their generalized Q-spectrum

On the Fractional Parts of Polynomials Modulo $p$

The $p$ -rationality of $Q (- (k p + m))$ and $Q (p (p + 1))$

Inequalities for $ζ (s) - ψ (1 - s)$ related to a conjecture of Henry

Trigonometric Determinants via special values of Dirichlet $L$ -Functions

Central $L$ values of congruent number elliptic curves

A new approach for constructing graph being determined by their generalized $Q$ -spectrum