一致收敛狄利克雷级数平移的刚性定理
A rigidity theorem for translates of uniformly convergent Dirichlet series
摘要：
众所周知，黎曼ζ函数，以及其他几个$L$ -函数，在带$1/2<σ<1$中是通用的;这当然不是真的$σ>1$。讨论了Bubieri和Ghosh的一个问题，给出了绝对收敛半平面上解析函数可由$L$ -函数平移逼近的一个简单刻画.实际上，这是狄利克雷级数平移的一般刚性定理在一致收敛性半平面上的一个特例。我们的结果与玻尔的等价定理密切相关。
英文摘要：
It is well known that the Riemann zeta function, as well as several other $L$-functions, is universal in the strip $1/2<σ<1$; this is certainly not true for $σ>1$. Answering a question of Bombieri and Ghosh, we give a simple characterization of the analytic functions approximable by translates of $L$-functions in the half-plane of absolute convergence. Actually, this is a special case of a general rigidity theorem for translates of Dirichlet series in the half-plane of uniform convergence. Our results are closely related to Bohr's equivalence theorem.
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