One-level density of families of elliptic curves and the Ratios Conjecture

DOI10.1007/S40993-015-0005-7zbMath1378.11066arXiv1309.1027OpenAlexW1863376393WikidataQ59433585 ScholiaQ59433585MaRDI QIDQ680039

Chantal David, Duc Khiem Huynh, James Parks

Publication date: 22 January 2018

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.1027

zbMATH Keywords

elliptic curveChebyshev polynomialone-level density\(L\)-functions attached to elliptic curvesRatios Conjectureroot number

Mathematics Subject Classification ID

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

Related Items (4)

Omega results for cubic field counts via lower-order terms in the one-level density ⋮ On the typical rank of elliptic curves over \(\mathbb{Q}(T)\) ⋮ Local statistics for zeros of Artin-Schreier 𝐿-functions ⋮ Low-lying zeros in families of elliptic curve \(L\)-functions over function fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An elliptic curve test of the \(L\)-functions ratios conjecture
• A unitary test of the Ratios Conjecture
• Autocorrelation of ratios of \(L\)-functions
• Lower order terms for the one-level density of elliptic curve \(L\)-functions
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Average rank of families of elliptic curves and Sato-Tate laws
• Surpassing the ratios conjecture in the 1-level density of Dirichlet \(L\)-functions
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• An orthogonal test of the L-functions Ratios Conjecture, II
• An orthogonal test of the L -functions Ratios conjecture
• Investigations of Zeros near the Central Point of Elliptic CurveL-Functions
• Class Numbers of the Simplest Cubic Fields
• The average rank of an algebraic family of elliptic curves
• Zeroes of zeta functions and symmetry
• Det-Det correlations for quantum maps: Dual pair and saddle-point analyses
• One- and two-level densities for rational families of elliptic curves: evidence for the underlying group symmetries
• Moments of the Critical Values of Families of Elliptic Curves, with Applications
• Applications of theL-functions ratios conjectures
• Notes on elliptic curves. II.
• Low-lying zeros of families of elliptic curves
• Low lying zeros of families of \(L\)-functions

This page was built for publication: One-level density of families of elliptic curves and the Ratios Conjecture