论文标题
在Balasubramanian-ramachandra方法上，接近re（s）= 1
On the Balasubramanian-Ramachandra method close to Re(s)=1
论文作者
论文摘要
我们研究了如何获得积分$$ \ int_t^{t+h} |ζ（σ+it）的良好估计值的问题。 DT，$$当$ h \ ll 1 $很小，$σ$接近$ 1 $，以及其他Dirichlet系列的相关积分，通过使用与Balasubramanian-Ramachandra方法相关的想法。我们使用由Paley-Fiener定理以及Ramachandra的内核函数构建的内核功能。我们还注意到，Ramachandra的内核功能的傅立叶变换实际上是$ k $ - 贝斯尔功能。这简化了Balasubramanian-Ramachandra方法的某些方面，因为它允许使用Bessel-intrunctions的理论。
We study the problem on how to get good lower estimates for the integral $$ \int_T^{T+H} |ζ(σ+it)| dt, $$ when $H \ll 1$ is small and $σ$ is close to $1$, as well as related integrals for other Dirichlet series, by using ideas related to the Balasubramanian-Ramachandra method. We use kernel-functions constructed by the Paley-Wiener theorem as well as the kernel function of Ramachandra. We also notice that the Fourier transform of Ramachandra's Kernel-function is in fact a $K$-Bessel function. This simplifies some aspects of Balasubramanian-Ramachandra method since it allows use of the theory of Bessel-functions.
