论文标题
Riesz类型标准$ L $ functions in Selberg类
Riesz type criteria for $L$-functions in the Selberg class
论文作者
论文摘要
我们在属于Selberg类的$ l $ functions中制定Riesz型标准的概括。我们获得了一个标准，该标准对于$ l $ functions满足Selberg类的公理而不将Ramanujan假设施加在其系数上的情况下，就足以满足$ l $ functions的大分假设（GRH）。我们还构建了Selberg类的子类，并证明了该子类中$ l $ functions的GRH的必要标准。在这种情况下，还建立了Ramanujan-Hardy-Littlewood类型的身份，其特定情况会产生新的转换公式，涉及Meijer $ G $ - 功能的特殊值$ G^{N \ 0} _ {0 \ n} $。
We formulate a generalization of Riesz-type criteria in the setting of $L$-functions belonging to the Selberg class. We obtain a criterion which is sufficient for the Grand Riemann Hypothesis (GRH) for $L$-functions satisfying axioms of the Selberg class without imposing the Ramanujan hypothesis on their coefficients. We also construct a subclass of the Selberg class and prove a necessary criterion for GRH for $L$-functions in this subclass. Identities of Ramanujan-Hardy-Littlewood type are also established in this setting, specific cases of which yield new transformation formulas involving special values of the Meijer $G$-function of the type $G^{n \ 0}_{0 \ n}$.
