We establish sharp upper bounds for the $2k$th moment of the Riemann zeta function on the critical line, for all real $0 \leqslant k \leqslant 2$. This improves on earlier work of Ramachandra, Heath-Brown and Bettin–Chandee–Radziwiłł.

中文翻译：

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RIEMANN ZETA函数的阶跃矩的锐利上界

对于所有真实的$ 0 \ leqslant k \ leqslant 2 $，我们在临界线上为黎曼zeta函数的第$ 2k $矩建立清晰的上限。这对Ramachandra，Heath-Brown和Bettin-Chandee-Radziwiłł的早期工作进行了改进。