It is well known that the Riemann zeta function, as well as several other $L$-functions, is universal in the strip $1/2 1$. 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.

中文翻译：

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一致收敛狄利克雷级数平移的刚性定理

众所周知，黎曼 zeta 函数以及其他几个 $L$ 函数在 $1/2 1$ 条带中是通用的。回答 Bombieri 和 Ghosh 的问题，我们给出了解析函数的简单表征，这些函数可通过在绝对收敛的半平面中平移 $L$ 函数来近似。实际上，这是狄利克雷级数在均匀收敛半平面上平移的一般刚性定理的一个特例。我们的结果与玻尔的等价定理密切相关。