Sato--Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height

William D. Banks, Igor E. Shparlinski

Type: Preprint

Publication Date: 2006-01-01

Citations: 5

DOI: https://doi.org/10.48550/arxiv.math/0609144

View Publication

Locations

arXiv (Cornell University) - View
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height	2009	William D. Banks Igor E. Shparlinski
+	On the average congruence class bias for cyclicity and divisibility of the groups of $\mathbb{F}_p$-points of elliptic curves	2023	Sung‐Min Lee
+ PDF Chat	Constants in Titchmarsh divisor problems for elliptic curves	2019	Renee Bell Clifford Blakestad Alina Carmen Cojocaru Alex Cowan Nathan Jones Vlad Matei Geoffrey Smith Isabel Vogt
+	Constants in Titchmarsh divisor problems for elliptic curves	2017	Renee Bell Clifford Blakestad Alina Carmen Cojocaru Alexander Cowan Nathan Jones Vlad Matei Geoffrey Smith Isabel Vogt
+	Constants in Titchmarsh divisor problems for elliptic curves	2017	Renee Bell Clifford Blakestad Alina Carmen Cojocaru Alex Cowan Nathan Jones Vlad Matei Geoffrey Smith Isabel Vogt
+	Cyclicity and exponent of elliptic curves modulo $p$ in arithmetic progressions	2023	Peng‐Jie Wong
+	Arithmetic statistics and diophantine stability for elliptic curves	2021	Anwesh Ray
+	On the Lang-Trotter and Sato-Tate conjectures on average for polynomial families of elliptic curves	2013	Igor E. Shparlinski
+	On the Lang-Trotter and Sato-Tate Conjectures on Average for Polynomial Families of Elliptic Curves	2012	Igor E. Shparlinski
+	On the Lang-Trotter and Sato-Tate Conjectures on Average for Polynomial Families of Elliptic Curves	2012	Igor E. Shparlinski
+	Refinements on vertical Sato-Tate	2023	Zhao Yu Ma
+	The Lang-Trotter Conjecture on Average	2006	Stephan Baier
+ PDF Chat	The Sato-Tate conjecture on average for small angles	2008	Stephan Baier Liangyi Zhao
+	The Sato-Tate Conjecture on Average for Small Angles	2006	Stephan Baier Liangyi Zhao
+	Class group statistics for torsion fields generated by elliptic curves	2022	Anwesh Ray Tom Weston
+	Asymptotics of the Tate-Shafarevich Group	2018	Shelly Manber
+	Average Cyclicity for Elliptic Curves in Torsion Families	2021	Luke Fredericks
+ PDF Chat	Watkins's conjecture for elliptic curves with a rational torsion	2024	Subham Bhakta Srilakshmi Krishnamoorthy
+ PDF Chat	The Frequency of Elliptic Curve Groups over Prime Finite Fields	2015	Vorrapan Chandee Chantal David Dimitris Koukoulopoulos Ethan Smith
+ PDF Chat	Opposing Average Congruence Class Biases in the Cyclicity and Koblitz Conjectures for Elliptic Curves	2024	Sung‐Min Lee Jacob Mayle Tian Wang

Works That Cite This (5)

Action	Title	Year	Authors
+	A Remark on the Conjectures of Lang-Trotter and Sato-Tate on Average	2007	Stephan Baier
+	Distribution of Farey fractions in residue classes and Lang–Trotter conjectures on average	2008	Alina Carmen Cojocaru Igor E. Shparlinski
+	On the Distribution of the Number of Points on Algebraic Curves in Extensions of Finite Fields	2009	Omran Ahmadi Igor E. Shparlinski
+	Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average	2007	Alina Carmen Cojocaru Igor E. Shparlinski
+	The Sato-Tate Conjecture on Average for Small Angles	2006	Stephan Baier Liangyi Zhao

Works Cited by This (24)

Action	Title	Year	Authors
+ PDF Chat	The Arithmetic of Elliptic Curves	1986	Joseph H. Silverman
+	Elements of number theory	1954	Ivan Matveevich Vinogradov Saul Kravetz
+	A Remark on the Conjectures of Lang-Trotter and Sato-Tate on Average	2007	Stephan Baier
+	The Lang-Trotter Conjecture on Average	2006	Stephan Baier
+ PDF Chat	On the Distribution of Supersingular Primes	1996	Étienne Fouvry M. Ram Murty
+	Cyclicity of CM elliptic curves modulo 𝑝	2003	Alina Carmen Cojocaru
+	Reductions of an elliptic curve and their Tate-Shafarevich groups	2004	Alina Carmen Cojocaru William Duke
+ PDF Chat	Factoring Integers with Elliptic Curves	1987	H. W. Lenstra
+	Mean behaviour and distribution properties of multiplicative functions	2004	K.‐H. Indlekofer Stefan Wehmeier Lutz Lucht
+ PDF Chat	The Square Sieve and the Lang–Trotter Conjecture	2005	Alina Carmen Cojocaru Étienne Fouvry M. Ram Murty