Uniform results for Serre's theorem for elliptic curves

By Alina Carmen Cojocaru, Chris Hall. 2005

57 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/154b909880fe9d73880a38eb895f5d4fdb12e1c1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. 'Alvaro Lozano-Robledo
2. Igor E. Shparlinski
3. N. Jones
4. Bjorn Poonen
5. Eric M. Rains

In Geometry and Topology

1. 'Alvaro Lozano-Robledo
2. Igor E. Shparlinski
3. N. Jones
4. Richard A. Brualdi
5. Bjorn Poonen
6. Eric M. Rains

Citations in the corpus

• ALMOST ALL ELLIPTIC CURVES ARE SERRE CURVES (2006, background): “Cojocaru and Hall [3] prove a similar result for elliptic curves in one-parameter families.”
• On the field of definition of $$p$$-torsion points on elliptic curves over the rationals (2013, background): “This question, usually known as “Serre’s uniformity problem”, has generated great interest (see [2], [6], [7], [27], [32], [40]).”
• Modular hyperbolas (2011, methodology): “In turn, this result has been used in [63] to improve upper bounds of [62] for the Lang–Trotter conjectures on Frobenius traces and Frobenius fields “on average” over a one-parametric family of elliptic curves EA,B(t) : U 2 = V 3 + A(t)V +B(t) with some polynomials A(t), B(t) ∈ Z[t] when the variabl”