ON THE RANK OF QUADRATIC TWISTS OF ELLIPTIC CURVES OVER FUNCTION FIELDS

DOI10.1142/S1793042106000528zbMath1115.11030arXivmath/0503732OpenAlexW2094322161MaRDI QIDQ5483367

Emmanuel Kowalski

Publication date: 14 August 2006

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503732

zbMATH Keywords

Elliptic curves over function fieldsRank of elliptic curves

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Density theorems (11R45)

Related Items (10)

Average ranks of elliptic curves: Tension between data and conjecture ⋮ Most elliptic curves over global function fields are torsion free ⋮ INTEGRAL MONODROMY GROUPS OF KLOOSTERMAN SHEAVES ⋮ The geometric distribution of Selmer groups of elliptic curves over function fields ⋮ A conditional determination of the average rank of elliptic curves ⋮ Some aspects and applications of the Riemann hypothesis over finite fields ⋮ Distribution questions for trace functions with values in cyclotomic integers and their reductions ⋮ Big symplectic or orthogonal monodromy modulo \(\ell\) ⋮ Towards an `average' version of the Birch and Swinnerton-Dyer conjecture ⋮ The large sieve, monodromy and zeta functions of curves

Cites Work

• Geometric non-vanishing
• The generic irreducibility of the numerator of the zeta function in a family of curves with large monodromy
• Maximality of Galois actions for compatible systems
• Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
• Courbes elliptiques sur Q sans nombres premiers exceptionnels

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