论文标题
Hurwitz Zeta功能的通用性在绝对收敛的半平面上
Universality of the Hurwitz zeta-function on the half plane of absolute convergence
论文作者
论文摘要
让$ k $成为一个紧凑型套件，在半平面re $ $ $（s）> 0 $上具有连接的补充，让$ f $是$ k $的连续功能，$ k $是内部分析的。我们证明，对于任何参数，对于任何参数$ 0 <α<1，α\ neq \ frac 1 2 $，然后$ f（s）$可以由$ζ（1+it+iT+iδs，α）$ k $均匀地近似，$ t，$ t $ t，gue t，δ> 0 $ t，Δ> 0 $，where $ζ$（s，α）$ζ（s，α）$ DETOTE hursote teote hurwwitzzeta-fun。这是第一个已知的普遍性结果，也已知可以为Hurwitz Zeta功能提供代数非理性参数。
Let $K$ be a compact set with connected complement on the half-plane Re$(s)>0$, and let $f$ be a continuous function on $K$ which is analytic in its interior. We prove that for any parameter $0<α<1, α\neq \frac 1 2$ then $f(s)$ may be uniformly approximated arbitrarily closely by $ζ(1+iT+iδs,α)$ on $K$ for some $T,δ>0$, where $ζ(s,α)$ denote the Hurwitz zeta-function. This is the first known universality result that is also known to hold for the Hurwitz zeta-function with an algebraic irrational parameter.
