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This is a Quantitative Study study.

October 5, 2025Open Access

Minimal Mahler Measure in Quartic Galois Number Fields

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Density results show the relationship between the minimal Mahler measure and the discriminant of Galois quartic fields, enhancing understanding of number theory.
Conditional findings on densities are based on the ABC conjecture, while several results are unconditional, demonstrating differing levels of certainty.
The study focuses on minimal integral Mahler measures, significant in understanding properties of number fields and their associated discriminants.
Exploration of Galois quartic fields provides insights into the broader implications of algebraic number theory and conjectures in mathematics.

Implication

Research reveals conditional density results regarding Mahler measure in Galois quartic fields, suggesting implications for number theory.

Abstract

We explore the dependence of the minimal integral Mahler measure of Galois quartic fields on the discriminant of the field. We obtain density results which are conditional on the ABC conjecture as well as several unconditional results.

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Cite This Study

Paudel et al. (2025) studied this question.

synapsesocial.com/papers/68e24e6fd6d66a53c2473ec9 https://doi.org/10.48550/arxiv.2510.00295

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Implication

Research reveals conditional density results regarding Mahler measure in Galois quartic fields, suggesting implications for number theory.

Minimal Mahler Measure in Quartic Galois Number Fields

Key Points

Implication

Abstract

Discussion

Cite This Study

Minimal Mahler Measure in Quartic Galois Number Fields

Key Points

Implication

Abstract

Discussion

Cite This Study