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<p>We apply the resonance method to obtain large values of general exponential sums with positive coefficients. As applications, we show improved <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation>-bounds for Dirichlet and Piltz divisor problems, Gauss circle Problem, and error terms for the mean square of the Riemann zeta function and the Dirichlet <i>L</i>-functions.</p>

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Omega results for the divisor and circle problems using the resonance method

  • 期刊论文

  • 发表日期：

    2026年3月18日

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  • Kamalakshya Mahatab

摘要

We apply the resonance method to obtain large values of general exponential sums with positive coefficients. As applications, we show improved \(\Omega \) Ω -bounds for Dirichlet and Piltz divisor problems, Gauss circle Problem, and error terms for the mean square of the Riemann zeta function and the Dirichlet L-functions.