论文标题
绝对收敛的一半平面上的联合通用性
Joint universality on the half plane of absolute convergence
论文作者
论文摘要
我们证明了与Euler产品的Dirichlet系列的一般类别的绝对融合一半平面上的联合普遍性定理，除了垂直偏移，我们还允许缩放。这概括了我们最近的Dirichlet $ L $ functions的联合普遍性结果。与古典普遍性相反，我们不需要所讨论的Dirichlet系列具有超出其绝对收敛区域的分析延续。此外，与Lee-Nakamura-Pańkowski的以前的联合普遍性结果相比，对成对的Dirichlet系列的正交条件较弱。我们要注意避免在我们的证明中使用Ramanujan的猜想，因此由于我们的普遍性定理，我们在绝对收敛的一半平面上比Booker-Thorne和Righetti的先前结果获得了$ L $ functions的线性组合的零结果。例如，由于我们的主要普遍性结果，我们有来自Maass Wave形式的Hecke $ l $ series的某些线性组合在任何条带中都有许多零零$ 1 <$ re $ $ re $ $ $（s）<1+δ$。
We prove joint universality theorems on the half plane of absolute convergence for general classes of Dirichlet series with an Euler-product, where in addition to vertical shifts we also allow scaling. This generalizes our recent joint universality results for Dirichlet $L$-functions. In contrast to classical universality, we do not need that the Dirichlet series in question have an analytic continuation beyond their region of absolute convergence. Also we may allow weaker orthogonality conditions for pairs of Dirichlet series than in the previous joint universality results of Lee-Nakamura-Pańkowski. We take care to avoid using the Ramanujan conjecture in our proof and hence as a consequence of our universality theorem, we obtain stronger results on zeros of linear combinations of $L$-functions in the half plane of absolute convergence than previous results of Booker-Thorne and Righetti. For example as a consequence of our main universality result we have that certain linear combinations of Hecke $L$-series coming from Maass wave forms have infinitely many zeros in any strip $1<$Re$(s)<1+δ$.
