Minimal Mahler Measure in Quartic Galois Number Fields

Key Points

• 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.