ROOT NUMBERS AND RANKS IN POSITIVE CHARACTERISTIC B. CONRAD, K. CONRAD, AND H. HELFGOTT Abstract. For a global field K and an elliptic curve Eη over K(T ), Silverman’s specialization theorem implies rank(Eη (K(T )))

Source URL: math.stanford.edu

• Group theory
• Diophantine geometry
• Algebraic curves
• Abelian variety
• Birch and Swinnerton-Dyer conjecture
• Supersingular elliptic curve
• Finite field
• Separable extension
• Lenstra elliptic curve factorization
• Abstract algebra
• Elliptic curves
• Number theory

Results from MathSciNet: Mathematical Reviews on the Web c Copyright American Mathematical Society 2005 MR2085902 11G40 11G10 Agashe, Amod (1-TX) ;

Source URL: wstein.org

• Number theory
• Elliptic curves
• Analytic number theory
• Abelian varieties
• Diophantine geometry
• Birch and Swinnerton-Dyer conjecture
• Tate–Shafarevich group
• Modular form
• Arithmetic of abelian varieties
• Abstract algebra
• Mathematics
• Algebraic geometry

References [1] Bernardi, D., Perrin-Riou, B.: Variante p-adique de la conjecture de Birch et Swinnerton-Dyer (le cas supersingulier). C. R. Acad. Sci. Paris S´er. I Math[removed]), no. 3, 227–[removed]Besser, A.: Th

Source URL: www.math.sci.osaka-u.ac.jp

• Elliptic curves
• Field theory
• Algebraic geometry
• Algebraic number theory
• P-adic number
• Birch and Swinnerton-Dyer conjecture
• P-adic L-function
• Néron–Tate height
• Iwasawa theory
• Abstract algebra
• Mathematics
• Number theory

LECTURE 3. THE BIRCH AND SWINNERTON-DYER CONJECTURE FOR HASSE-WEIL-ARTIN L-FUNCTIONS. Abstract: The third lecture blends the themes of the previous two in order to discuss the Birch and Swinnerton-Dyer conjecture over th

Source URL: www.math.mcmaster.ca

LECTURE 2. ELLIPTIC CURVES AND THE BIRCH AND SWINNERTON-DYER CONJECTURE Abstract: The second lecture extends some of the themes explored in the first to the setting of elliptic curves, where it becomes important to repla

Source URL: www.math.mcmaster.ca

Explicit approaches to modular abelian varieties by William Arthur Stein

Source URL: wstein.org

• Modular forms
• Number theory
• Analytic number theory
• Algebraic curves
• Diophantine geometry
• Hecke operator
• Tate–Shafarevich group
• Elliptic curve
• Birch and Swinnerton-Dyer conjecture
• Abstract algebra
• Mathematics
• Algebraic geometry

Balanced subgroups of the multiplicative group Carl Pomerance, Dartmouth College

Source URL: www.math.dartmouth.edu

• Integer sequences
• Group theory
• Analytic number theory
• Finite fields
• Elliptic curve
• Prime number
• Factorial
• Lenstra elliptic curve factorization
• Birch and Swinnerton-Dyer conjecture
• Mathematics
• Abstract algebra
• Number theory

Balanced subgroups of the multiplicative group Carl Pomerance, Dartmouth College

Source URL: www.math.dartmouth.edu

• Integer sequences
• Analytic number theory
• Group theory
• Elliptic curve
• Finite fields
• Factorial
• Prime number
• Lenstra elliptic curve factorization
• Birch and Swinnerton-Dyer conjecture
• Mathematics
• Abstract algebra
• Number theory

KEVIN JAMES Assistant Professor Mathematical Sciences

Source URL: www.math.clemson.edu

• Analytic number theory
• Conjectures
• Elliptic curves
• Algebraic curves
• Modular forms
• Birch and Swinnerton-Dyer conjecture
• Modular curve
• Sato–Tate conjecture
• Number theory
• Abstract algebra
• Mathematics
• Mathematical analysis

Elliptic Curves over Q Steven Finch October 10, 2005 All polynomials and rational functions in this essay are assumed to have coefficients in Q. Fix an integer n ≥ 1. An affine variety is a simultaneous irreducible sys

Source URL: www.people.fas.harvard.edu

• Analytic number theory
• Elliptic curves
• Group theory
• Elliptic curve cryptography
• Algebraic curves
• Elliptic curve
• Abelian variety
• Birch and Swinnerton-Dyer conjecture
• Tripling-oriented Doche–Icart–Kohel curve
• Abstract algebra
• Algebraic geometry
• Mathematics