\(p\)-adic properties of division polynomials and elliptic divisibility sequences

DOI10.1007/s00208-004-0608-0zbMath1066.11024arXivmath/0404412OpenAlexW2091908303MaRDI QIDQ1779179

Joseph H. Silverman

Publication date: 1 June 2005

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0404412

zbMATH Keywords

elliptic curvesdivision polynomialselliptic divisibility sequences

Mathematics Subject Classification ID

Elliptic curves (14H52) Finite ground fields in algebraic geometry (14G15) Local ground fields in algebraic geometry (14G20) Elliptic curves over local fields (11G07)

Related Items (12)

ALGEBRAIC DIVISIBILITY SEQUENCES OVER FUNCTION FIELDS ⋮ Sigma function solution of the initial value problem for Somos 5 sequences ⋮ The elliptic sieve and Brauer groups ⋮ On the product of translated division polynomials and Somos sequences ⋮ Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences ⋮ Elliptic nets and elliptic curves ⋮ Analytic solutions and integrability for bilinear recurrences of order six ⋮ Sequences associated to elliptic curves with non-cyclic torsion subgroup ⋮ Unnamed Item ⋮ Primitive Divisors on Twists of Fermat's Cubic ⋮ The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences ⋮ Generalized greatest common divisors, divisibility sequences, and Vojta's conjecture for blowups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The existence of infinitely many supersingular primes for every elliptic curve over \(\mathbb Q\).
• Quelques applications du théorème de densité de Chebotarev
• Explicit valuations of division polynomials of an elliptic curve
• The canonical height of an algebraic point on an elliptic curve
• The \(p\)-adic sigma function
• Sequences of numbers generated by addition in formal groups and new primality and factorization tests
• The law repetition of primes in an elliptic divisibility sequence
• Primes in Elliptic Divisibility Sequences
• A Full Characterisation of Divisibility Sequences
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• Periodicity of Somos Sequences
• Memoir on Elliptic Divisibility Sequences
• The Apparition Problem for Equianharmonic Divisibility Sequences

This page was built for publication: \(p\)-adic properties of division polynomials and elliptic divisibility sequences