论文标题
Bombieri的无原木密度估算和Sárközy的定理的明确版本
An explicit version of Bombieri's log-free density estimate and Sárközy's theorem for shifted primes
论文作者
论文摘要
对于dirichlet $ l $ functions，我们将明确的Bombieri对Gallagher的无原木密度估计接近$σ= 1 $”进行了明确的改进。我们使用这项估计和最新的绿色工作来证明，如果$ n \ geq 2 $是整数，$ a \ subseteq \ {1，\ ldots，n \} $，对于所有普通$ p $ p $ no $ a $ a $ a $ a $ a $ a $ a $ a $ p-1的两个要素，则由$ p-1差异，然后由$ p-1 $，然后是$ | a | \ ll n^^^1-1-1-1-1-1/10^}}。这加强了萨尔科兹的定理。
We make explicit Bombieri's refinement of Gallagher's log-free "large sieve density estimate near $σ= 1$" for Dirichlet $L$-functions. We use this estimate and recent work of Green to prove that if $N\geq 2$ is an integer, $A\subseteq\{1,\ldots,N\}$, and for all primes $p$ no two elements in $A$ differ by $p-1$, then $|A|\ll N^{1-1/10^{18}}$. This strengthens a theorem of Sárközy.
