Almost cubes and fourth powers in short intervals

Tsz Ho Chan

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arXiv · 2503.21490

Almost cubes and fourth powers in short intervals

Tsz Ho Chan

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Abstract

In this paper, we study how short an interval $[x, x + x^θ]$ contains an integer of the form $n_1 n_2 n_3$ and $m_1 m_2 m_3 m_4$ with $n_1 \approx n_2 \approx n_3$ and $m_1 \approx m_2 \approx m_3 \approx m_4$. The new idea is to adopt a second moment method (usually used for almost all results) to deduce a result for all short intervals.

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BibTeX RIS

Tsz Ho Chan. 2025-03-27. Almost cubes and fourth powers in short intervals. https://arxiv.org/abs/2503.21490

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