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An extended Vinogradov’s mean value theorem

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This work provides upper bounds for exponential sums using Hardy-Littlewood circle method, suggesting advances in mean value theorem applications.

Upper bounds for exponential sums in the context of the mean value theorem were established using detailed mathematical methods.
The study focused on exponential sums defined through coefficients, demonstrating significant bounds for natural numbers d ≥ 2.
Employing the Hardy-Littlewood circle method, new estimates were derived for mean values applicable to conjectures related to the theorem.
Findings indicate a refined approach to handling exponential sums, particularly for cases where d equals 2 or 3, and adapting for higher dimensions.

Oh et al. (2025) studied this question.

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View Full Paper

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Authors

This work provides upper bounds for exponential sums using Hardy-Littlewood circle method, suggesting advances in mean value theorem applications.

Upper bounds for exponential sums in the context of the mean value theorem were established using detailed mathematical methods.
The study focused on exponential sums defined through coefficients, demonstrating significant bounds for natural numbers d ≥ 2.
Employing the Hardy-Littlewood circle method, new estimates were derived for mean values applicable to conjectures related to the theorem.
Findings indicate a refined approach to handling exponential sums, particularly for cases where d equals 2 or 3, and adapting for higher dimensions.

Oh et al. (2025) studied this question.

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