A conjectural improvement for inequalities related to regulators of number fields

Francesco Battistoni*

*Corresponding author

Research output: Contribution to journalArticle

Abstract

An inequality proved firstly by Remak and then generalized by Friedman shows that there are only finitely many number fields with a fixed signature and whose regulator is less than a prescribed bound. Using this inequality, Astudillo, Diaz y Diaz, Friedman and Ramirez-Raposo succeeded to detect all fields with small regulators having degree less or equal than 7. In this paper we show that a certain upper bound for a suitable polynomial, if true, can improve Remak–Friedman’s inequality and allows a classification for some signatures in degree 8 and better results in degree 5 and 7. The validity of the conjectured upper bound is extensively discussed.
Original languageEnglish
Pages (from-to)609-627
Number of pages19
JournalBOLLETTINO DELLA UNIONE MATEMATICA ITALIANA
Volume14
DOIs
Publication statusPublished - 2021

Keywords

  • Number fields
  • Regulators
  • Upper bounds

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