The Sato–Tate distribution in thin parametric families of elliptic curves

Régis de la Bretèche, Min Sha*, Igor E. Shparlinski, José Felipe Voloch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We obtain new results concerning the Sato–Tate conjecture on the distribution of Frobenius traces over single and double parametric families of elliptic curves. We consider these curves for values of parameters having prescribed arithmetic structure: product sets, geometric progressions, and most significantly prime numbers. In particular, some families are much thinner than the ones previously studied.

Original languageEnglish
Pages (from-to)831-855
Number of pages25
JournalMathematische Zeitschrift
Volume290
Issue number3-4
Early online date8 Mar 2018
DOIs
Publication statusPublished - Dec 2018
Externally publishedYes

Keywords

  • Parametric families of elliptic curves
  • Sato–Tate conjecture

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