We give an elementary exposition of the little known work of Harold Davenport related to Hasse’s inequality. We formulate a new conjecture suggested by this proof that has implications for the classical Riemann hypothesis.

中文翻译：

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关于 Hasse 的不等式

我们对 Harold Davenport 鲜为人知的与 Hasse 不等式相关的工作进行了初步阐述。我们根据这个证明提出了一个新的猜想，它对经典黎曼假设有影响。