Li Long

collaborators

8 papers

math.NT2026

A quaternary Diophantine inequality with prime numbers of a special form (II)

Yuhua Zhao, Jinjiang Li, Linji Long +1

Let $N$ be a sufficiently large real number. In this paper, it is proved that, for $1 < c < \frac{5179}{3909}$ and for any arbitrary large number $E > 0$ , the Diophantine inequality \beg…

math.NT2026

On a variant of the Piatetski-Shapiro prime number theorem

Linji Long, Jinjiang Li, Min Zhang

Denote by $Π_{γ} (x)$ the number of primes $p ⩽ x$ such that $[p^{1/ γ}]$ is also a prime. In this paper, it is proved that the expected asymptotic formula \begin{equation*} Π_…

math.PR2026

Weak universality of global dynamics for the fractional hyperbolic $Φ_{3}^{4}$ -model

Ruoyuan Liu

We continue the study of weak universality for the fractional hyperbolic $Φ_{3}^{4}$ -model initiated by Tzvetkov, Wang, and the author (2023). In this work, we establish weak universal…

math.NT2026

On Piatetski-Shapiro primes from almost primes

Yuhua Zhao, Jinjiang Li, Linji Long +1

Denote by $P_{r}$ an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this manuscript, it is established that, for any fixed $0.98353 < γ < 1$ …

math.NT2026

On the quadratic Waring-Goldbach problem with primes in Piatetski-Shapiro sets

Meng Gao, Jinjiang Li, Linji Long +1

In this paper, it is proved that, for any $γ_{1}, γ_{2}, γ_{3}, γ_{4}, γ_{5} \in (\frac{28}{29}, 1)$ , every sufficiently large integer $n$ subject to $n \equiv 5 (mod 24)$ can be represented as the s…

math.NT2025

Cubic Waring-Goldbach problem with Piatetski-Shapiro primes

Linji Long, Jinjiang Li, Min Zhang +1

In this paper, it is proved that, for $γ \in (\frac{317}{320}, 1)$ , every sufficiently large odd integer can be written as the sum of nine cubes of primes, each of which is of the for…

math.NT2025

On the mean square of the error term for the asymmetric two-dimensional divisor problem with congruence conditions

Zhen Guo, Jinjiang Li, Linji Long +1

Suppose that $a$ and $b$ are positive integers subject to $(a, b) = 1$ . For $n \in Z^{+}$ , denote by $τ_{a, b} (n; ℓ_{1}, M_{1}, l_{2}, M_{2})$ the asymmetric two--dimensional divisor funct…

math.NT2025

On a system of two Diophantine inequalities with six prime variables

Linji Long, Jinjiang Li, Min Zhang +1

Suppose that $c, d, α, β$ are real numbers satisfying the inequalities $1 < d < c < 79/71$ and $1 < α < β < 6^{1 - d / c}$ . In this paper, it is proved that, for sufficiently large real numbers $N_{1}$ …

A quaternary Diophantine inequality with prime numbers of a special form (II)

On a variant of the Piatetski-Shapiro prime number theorem

Weak universality of global dynamics for the fractional hyperbolic Φ34​-model

On Piatetski-Shapiro primes from almost primes

On the quadratic Waring-Goldbach problem with primes in Piatetski-Shapiro sets

Cubic Waring-Goldbach problem with Piatetski-Shapiro primes

On the mean square of the error term for the asymmetric two-dimensional divisor problem with congruence conditions

On a system of two Diophantine inequalities with six prime variables

Weak universality of global dynamics for the fractional hyperbolic $Φ_{3}^{4}$ -model