论文标题
Helson Zeta功能有限多个值的字符功能
Helson zeta functions for characters with finitely many values
论文作者
论文摘要
我们表明，Helson Zeta功能的分析延续$ζ_χ（s）= \ sum_1^{\ infty}χ（n）n^{ - s} $在本质上可以在$ 21/40 <\ re s <1 $的$ 21/40 <\ re Reim $ 1/2 <\ reie $ 1/2/2/2 << $χ$以团结的立方根为基础。如果这些集合相对于真实轴对称，则可以使用$ \ $的$ \ pm 1 $来实现相同的情况。
We show that the analytic continuations of Helson zeta functions $ ζ_χ(s)= \sum_1^{\infty}χ(n)n^{-s} $ can have essentially arbitrary poles and zeroes in the strip $ 21/40 < \Re s < 1 $ (unconditionally), and in the whole critical strip $ 1/2 < \Re s <1 $ under Riemann Hypothesis for the function $ χ$ taking values in cubic roots of unity. If the sets are symmetric with respect to the real axis, the same can be achieved with $ χ$ taking values $ \pm 1 $.
