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LOWER BOUNDS FOR THE MAHLER MEASURE AND INERTIA DEGREES OF PRIMES
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SHANTA LAISHRAM, GOREKH PRASAD
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Bulletin of the Australian Mathematical Society , First View

Published online by Cambridge University Press:

02 December 2024, pp. 1-12
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We investigate the relationship between lower bounds for the Mahler measure and splitting of primes, and prove various lower bounds for the Mahler measure of algebraic integers in terms of the least common multiples of all inertia degrees of primes. The results generalise work of the second author and Kumar [‘Lehmer’s problem and splitting of rational primes in number fields’, Acta Math. Hungar. 169(2) (2023), 349–358].

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LOWER BOUNDS FOR THE MAHLER MEASURE AND INERTIA DEGREES OF PRIMES