Bin Chen

activity

20232025

collaborators

4 papers

math.NT2025

Large Value Estimates for Dirichlet Polynomials with Characters and Zero Density of Dirichlet $L$ -Functions

Bin Chen, Vishal Gupta, Yung Chi Li

It is proved that \[ \sum_{χ\bmod q}N(σ,T,χ) \ll_ε (qT)^{7(1-σ)/3+ε}, \] where $N (σ, T, χ)$ denotes the number of zeros $ρ = β + i t$ of $L (s, χ)$ in the rectangle $σ \leq β \leq 1$ , $|t|\le…

math.NT2024

Small gaps between almost-twin primes

Bin Chen

Let $m \in N$ be large. We show that there exist infinitely many primes $q_{1} < \cdot \cdot \cdot < q_{m + 1}$ such that \[ q_{m+1}-q_{1}=O(e^{7.63m}) \] and $q_{j} + 2$ has at…

math.CV2023

Generalizations of Koga's version of the Wiener-Ikehara theorem

Bin Chen, Jasson Vindas

We establish new versions of the Wiener-Ikehara theorem where only boundary assumptions on the real part of the Laplace transform are imposed. Our results generalize and improve a…

math.NT2023

On the density hypothesis for $L$ -functions associated with holomorphic cusp forms

Bin Chen, Gregory Debruyne, Jasson Vindas

We study the range of validity of the density hypothesis for the zeros of $L$ -functions associated with cusp Hecke eigenforms $f$ of even integral weight and prove that $N_{f}(σ, T…

Large Value Estimates for Dirichlet Polynomials with Characters and Zero Density of Dirichlet L-Functions

Small gaps between almost-twin primes

Generalizations of Koga's version of the Wiener-Ikehara theorem

On the density hypothesis for L-functions associated with holomorphic cusp forms

Large Value Estimates for Dirichlet Polynomials with Characters and Zero Density of Dirichlet $L$ -Functions

On the density hypothesis for $L$ -functions associated with holomorphic cusp forms