582e: Course References

General references

• The AWESOME book Surveys in algorithmic number theory

Number Fields

• William Stein's Algebraic Number Theory

• Chapter 4, Analytic Methods in Borevich and Shafarevich's Number Theory.

• Gary Sivek's student project The Analytic Class Number Formula for my class in 2005.

• Chapter X of Cohn's Advanced Number Theory is about the class number formula in the case of a quadratic field.

• Eric Bach's Explicit Bounds for Primality Testing and Related Problems

• Peter Stevenhagen's The Arithmetic of Number Rings

Elliptic Curves

• William Stein's The Birch and Swinnerton-Dyer Conjecture, a Computational Approach

• Andrei Jorza's Harvard senior thesis The Birch and Swinnerton-Dyer Conjecture for Abelian Varieties over Number Fields

• Andrei Jorza's The Analytic Class Number Formula and the Birch and Swinnerton-Dyer Conjecture

• Andrew Wiles's CMI Prize Problem Description about BSD

• Bryan Birch: Birch-Conjectures_Concerning_Elliptic_Curves.pdf

• Bryan Birch: Birch-Elliptic_curves_over_Q-A_Progress_Report.pdf

• Antwerp tables: http://modular.math.washington.edu/Tables/antwerp/

• Cremona's tables: http://www.warwick.ac.uk/staff/J.E.Cremona//ftp/data/INDEX.html and http://www.ma.utexas.edu/users/tornaria/cnt/cremona.html

• William Stein et al.: Verification of the Birch and Swinnerton-Dyer Conjecture for Specific Elliptic Curves

• Stein-Watkins data: http://wstein.org/Tables/ecdb/stein-watkins-ecdb/ (there are also 3 articles about this data)