Minimal Mahler measure in cubic number fields

Lydia Eldredge, Kathleen Petersen

Research output: Contribution to journalArticlepeer-review

Abstract

The minimal integral Mahler measure of a number field K, M(K), is the minimal Mahler measure of an integral generator of K. Upper and lower bounds, which depend on the discriminant and degree of K, are known. We show that for three natural families of cubics, the lower bounds are sharp with respect to its growth as a function of discriminant. We construct an algorithm to compute M(K) for all cubics with absolute value of the discriminant bounded by N and show the resulting data for N = 10, 000.

Original languageEnglish (US)
Pages (from-to)2157-2169
Number of pages13
JournalInternational Journal of Number Theory
Volume18
Issue number10
DOIs
StateAccepted/In press - 2022

Bibliographical note

Funding Information:
Kathleen Petersen was supported by Simons Foundation Grant 430077

Publisher Copyright:
© 2022 World Scientific Publishing Company.

Keywords

  • Mahler measure
  • Weil height
  • cubic number fields

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