Xue-Jun Guo

activity

20232026

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5 papers · 1 filter

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…

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

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