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 A Few Equivalent Statements of a Hilbert-Type Integral Inequality with the Riemann Zeta Function Weiliang Wu,Bicheng Yang Keywords:Hilbert-type integral inequality; weight function; intermediate variable; equivalent statement; operator; Riemann zeta function Abstract: By using the way of real analysis and the weight functions, a few equivalent statements of a Hilbert-type integral inequality in the whole plane with the intermediate variables and the best possible constant factor related to the Riemann zeta function is proved. Some particular cases and the operator expression are considered.