Applications of the Square Sieve to a Conjecture of Lang and Trotter for a Pair of Elliptic Curves Over the Rationals

DOI10.1007/978-3-319-97379-1_3zbMath1475.11170arXiv1710.02125OpenAlexW2964088792MaRDI QIDQ5014817

Vijay M. Patankar, Stephan Baier

Publication date: 8 December 2021

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.02125

Mathematics Subject Classification ID

Asymptotic results on counting functions for algebraic and topological structures (11N45) Elliptic curves over global fields (11G05) Applications of sieve methods (11N36) Density theorems (11R45)

Related Items (1)

The Lang-Trotter conjecture for products of non-CM elliptic curves

Cites Work

• Locally potentially equivalent two dimensional Galois representations and Frobenius fields of elliptic curves
• The square sieve and consecutive square-free numbers
• Quelques applications du théorème de densité de Chebotarev
• Frobenius distributions in \(\mathrm{GL}_2\)-extensions. Distribution of Frobenius automorphisms in \(\mathrm{GL}_2\)-extensions of the rational numbers
• Galois properties of points of finite order of elliptic curves
• The Square Sieve and the Lang–Trotter Conjecture
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