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

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

doi:10.1007/s00209-018-2042-0

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 journal › Article › peer-review

4 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 language	English
Pages (from-to)	831-855
Number of pages	25
Journal	Mathematische Zeitschrift
Volume	290
Issue number	3-4
Early online date	8 Mar 2018
DOIs	https://doi.org/10.1007/s00209-018-2042-0
Publication status	Published - Dec 2018
Externally published	Yes

Keywords

Parametric families of elliptic curves
Sato–Tate conjecture

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10.1007/s00209-018-2042-0

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title = "The Sato–Tate distribution in thin parametric families of elliptic curves",

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.",

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year = "2018",

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AU - de la Bretèche, Régis

AU - Sha, Min

AU - Shparlinski, Igor E.

AU - Voloch, José Felipe

PY - 2018/12

Y1 - 2018/12

N2 - 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.

AB - 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.

KW - Parametric families of elliptic curves

KW - Sato–Tate conjecture

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DO - 10.1007/s00209-018-2042-0

M3 - Article

AN - SCOPUS:85043358622

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VL - 290

SP - 831

EP - 855

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

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

Abstract

Keywords

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