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There are several consequences of the Riemann hypothesis in many area as Number theory , complex analysis $\cdots $ ,I'm interesting to know what about those consequences if the Riemann zeta function satisfy any known Algebraic differential equation then what are the contributions of Riemann Hypothesis to physics if the Riemann zeta function is a solution for known differential equation?

Note: I meant here by satisfies any algebraic differential equation that zeta function is a solution for known algebraic differential equation

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