论文标题
在Riemann Zeta功能的某些傅立叶扩展上
On certain Fourier expansions for the Riemann zeta function
论文作者
论文摘要
我们以有关Riemann Zeta功能的傅立叶扩展的最新论文为基础。我们为某些$ l $ functions建立了傅立叶扩展，并提供涉及whittaker函数$ W_ {γ，μ}（z）$的系列表示。还陈述了Riemann Zeta功能的倒数的傅立叶扩展。第三部分通过使用Mellin Transforms为其傅立叶系数构建积分公式，为Riemann XI函数提供了新的扩展。
We build on a recent paper on Fourier expansions for the Riemann zeta function. We establish Fourier expansions for certain $L$-functions, and offer series representations involving the Whittaker function $W_{γ,μ}(z)$ for the coefficients. Fourier expansions for the reciprocal of the Riemann zeta function are also stated. A new expansion for the Riemann xi function is presented in the third section by constructing an integral formula using Mellin transforms for its Fourier coefficients.
