Extremal primes for elliptic curves

DOI10.1016/j.jnt.2016.01.009zbMath1416.11081OpenAlexW2289673113MaRDI QIDQ266615

Minh-Tam Trinh, Dania Zantout, Phil Wertheimer, Brandon Tran, Kevin L. James

Publication date: 13 April 2016

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2016.01.009

zbMATH Keywords

elliptic curvesdistribution of primesLang-Trotter conjectureFrobenius distributionstrace of Frobenius

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Distribution of primes (11N05)

Related Items (7)

Frobenius distributions of elliptic curves in short intervals on average ⋮ The absolute discriminant of the endomorphism ring of most reductions of a non-CM elliptic curve is close to maximal ⋮ Extremal primes for elliptic curves with complex multiplication ⋮ Equidistribution of αpθ$\alpha p^{\theta }$ with a Chebotarev condition and applications to extremal primes ⋮ Frobenius distributions in short intervals for CM elliptic curves ⋮ Almost all primes satisfy the Atkin-Serre conjecture and are not extremal ⋮ Extremal primes for elliptic curves without complex multiplication

Cites Work

• A family of Calabi-Yau varieties and potential automorphy. II.
• A family of Calabi-Yau varieties and potential automorphy
• Automorphy for some \(l\)-adic lifts of automorphic mod \(l\) Galois representations. With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras.
• Automorphy for some \(l\)-adic lifts of automorphic mod \(l\) Galois representations. II
• Frobenius distributions in \(\mathrm{GL}_2\)-extensions. Distribution of Frobenius automorphisms in \(\mathrm{GL}_2\)-extensions of the rational numbers
• Distribution of values of Hecke characters of infinite order
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