# 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)