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arXiv · 2504.17032

Omega Results for The Divisor and Circle Problems Using The Resonance Method

Kamalakshya Mahatab
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Abstract

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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Kamalakshya Mahatab. 2025-04-23. Omega Results for The Divisor and Circle Problems Using The Resonance Method. https://arxiv.org/abs/2504.17032

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