Omega Results for The Divisor and Circle Problems Using The Resonance Method
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math.NT
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circledirichletdivisorfunctionmethodomegaproblemsresonance
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We apply the resonance method to obtain large values of general exponential sums with positive coefficients. As applications, we show improved $\Omega$-bounds for Dirichlet and Piltz divisor problems, Gauss circle Problem, and error term for the mean square of the Riemann zeta function and the Dirichlet $L$-function.
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