A NOTE ON RH FOR CURVES AND HYPERSURFACES OVER FINITE FIELDS NICHOLAS M. KATZ Abstract. We give what is arguably a simple (though certainly not elementary, cf. [Sch]) proof of the Riemann Hypothesis for (projective, smoo

Source URL: web.math.princeton.edu

• Linear algebra
• Matrix theory
• Finite fields
• Genus of a multiplicative sequence
• Eigenvalues and eigenvectors
• Elliptic curve
• Weil conjectures
• Profinite group

A THEORY OF ORDINARY P-ADIC CURVES A Theory of Ordinary p-adic Curves By Shinichi MOCHIZUKI*

Source URL: www.kurims.kyoto-u.ac.jp

• Algebraic geometry
• Complex analysis
• Riemann surfaces
• Vector bundles
• Algebraic varieties
• Canonical bundle
• Beltrami equation
• Indigenous bundle
• Ample line bundle
• Supersingular elliptic curve
• Differential geometry of surfaces
• Chern class

Isogenies and endomorphism rings of elliptic curves ECC Summer School Damien Robert Microsoft ResearchNancy)

Source URL: www.normalesup.org

• Elliptic curves
• Algebraic curves
• Analytic number theory
• Algebraic surfaces
• Supersingular elliptic curve
• Elliptic curve
• Isogeny
• Abelian variety
• Supersingular variety
• Supersingular isogeny key exchange
• Elliptic curve cryptography

How Euler Did It by Ed Sandifer Arc length of an ellipse October, 2004 It is remarkable that the constant, π, that relates the radius to the circumference of a circle in the familiar formula C = 2π r is the same consta

Source URL: eulerarchive.maa.org

• Curves
• Elliptic functions
• Ellipse
• Integral calculus
• Complex analysis
• Elliptic integral
• Area of a circle
• Arc length
• Jacobi elliptic functions
• Triangle
• Pi
• Gamma function

Primality Testing Using Elliptic Curves SHAFI GOLDWASSER Massachusetts Institute of Technology, Cambridge, Massachusetts AND JOE KILIAN

Source URL: www.mat.uniroma2.it

• Primality tests
• Finite fields
• Probabilistic complexity theory
• Modular arithmetic
• Group theory
• Primality certificate
• Prime number
• Elliptic curve primality
• Elliptic curve
• SolovayStrassen primality test
• Number theory
• Randomized algorithm

Endomorphism rings of elliptic curves over finite fields by David Kohel B.S. Biochemstry (Texas A&M UniversityB.S. Mathematics (Texas A&M University) 1989

Source URL: iml.univ-mrs.fr

• Elliptic curves
• Finite fields
• Supersingular elliptic curve
• Group theory
• Elliptic curve cryptography
• Algebraic number theory
• Elliptic curve
• Complex multiplication
• Supersingular variety
• Frobenius endomorphism
• Group scheme
• Twists of curves

On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields David R. Kohel1 and Igor E. Shparlinski2 1 School of Mathematics and Statistics

Source URL: iml.univ-mrs.fr

• Group theory
• Analytic number theory
• Elliptic curve
• Operator theory
• Differential forms on a Riemann surface
• Linear temporal logic

Commun. Math. Phys. 229, 459–Digital Object Identifier (DOIs00220Communications in Mathematical

Source URL: www-irma.u-strasbg.fr

• Algebra
• Mathematics
• Geometry
• Algebraic curves
• Complex analysis
• Differential geometry
• Algebraic surfaces
• PicardLefschetz theory
• Elliptic curve
• Abelian variety
• Monodromy
• Curve

QUADRATIC FORMS AND ELLIPTIC CURVES III KEN ONO# and TAKASHI ONO There have been many investigations regarding the distribution of ranks of elliptic curves in natural families, and it is believed that the vast majority

Source URL: www.mathcs.emory.edu

Smaller class invariants for constructing curves of genus 2 Marco Streng The 15th workshop on Elliptic Curve Cryptography

Source URL: ecc2011.loria.fr

• Abstract algebra
• Algebra
• Geometry
• Elliptic curve cryptography
• Elliptic curves
• Algebraic curves
• Group theory
• Algebraic surfaces
• Complex multiplication
• Elliptic curve
• Curve
• Abelian variety