Bin Chen

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math.NT2025

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.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 \[ \sum_{Ï\bmod q}N(Ï,T,Ï) \ll_Îµ (qT)^{7(1-Ï)/3+Îµ}, \] where $N (I ¨ , T, I ¨ )$ denotes the number of zeros $I ¨ = I^^{2} + i t$ of $L (s, I ¨ )$ in the rectangle $Ï\leq Î²\le…

Small gaps between almost-twin primes

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

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