Legendre Drinfeld modules and universal supersingular polynomials

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Abstract

We introduce a certain family of Drinfeld modules that we propose as analogues of the Legendre normal form elliptic curves. We exhibit explicit formulas for a certain period of such Drinfeld modules as well as formulas for the supersingular locus in that family, establishing a connection between these two kinds of formulas. Lastly, we also provide a closed formula for the supersingular polynomial in the j-invariant for generic Drinfeld modules.

Original languageEnglish
Pages (from-to)1277-1289
Number of pages13
JournalInternational Journal of Number Theory
Volume10
Issue number5
DOIs
Publication statusPublished - 2014
Externally publishedYes

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Keywords

  • Legendre Drinfeld modules
  • periods
  • supersingularity

ASJC Scopus subject areas

  • Algebra and Number Theory

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