Motohashi established an explicit identity between the fourth moment of the Riemann zeta function weighted by some test function and a spectral cubic moment of automorphic L-functions. By an entirely different method, we prove a generalization of this formula to a fourth moment of Dirichlet L-functions modulo q weighted by a non-archimedean test function. This establishes a new reciprocity formula. As an application, we obtain sharp upper bounds for the fourth moment twisted by the square of a Dirichlet polynomial of length q^{1/4}. An auxiliary result of independent interest is a sharp upper bound for a certain sixth moment for automorphic L-functions, which we also use to improve the best known subconvexity bounds for automorphic L-functions in the level aspect.

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Motohashi 非阿基米德测试函数和应用的四阶矩恒等式

Motohashi 在由某个测试函数加权的黎曼 zeta 函数的四阶矩和自守 L 函数的谱三次矩之间建立了明确的恒等式。通过一种完全不同的方法，我们证明了该公式对由非阿基米德测试函数加权的狄利克雷 L 函数模 q 的四阶矩的推广。这建立了一个新的互惠公式。作为一个应用，我们获得了由长度为 q^{1/4} 的狄利克雷多项式的平方扭曲的四阶矩的尖锐上界。一个独立感兴趣的辅助结果是自守 L 函数的某个六阶矩的尖锐上界，我们也使用它来改进水平方面自守 L 函数的最知名的子凸边界。