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<p>We revisit a subexponential bound for the <i>abc</i> conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the 4-terms <i>abc</i> conjecture under a suitable hypothesis on the size of the variables.</p>

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On the abc and the abcd Conjectures

  • 期刊论文

  • 发表日期：

    2025年10月5日

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  • Hector Pasten,
  • Rocío Sepúlveda-Manzo

摘要

We revisit a subexponential bound for the abc conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the 4-terms abc conjecture under a suitable hypothesis on the size of the variables.