The \(p\)-adic sigma function

DOI10.1215/S0012-7094-91-06229-0zbMath0735.14020OpenAlexW2059480244WikidataQ101084267 ScholiaQ101084267MaRDI QIDQ1814235

John Tate, Barry Mazur

Publication date: 25 June 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-91-06229-0

zbMATH Keywords

formal groupcharacteristic pcanonical heightscomplex elliptic curvesp-adic theta functionsp-adic analog of the Weierstrass sigma function

Mathematics Subject Classification ID

Elliptic curves (14H52) Theta functions and abelian varieties (14K25) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Local ground fields in algebraic geometry (14G20) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items

"Equation missing" -Integral Points on a Mordell Curve, \(p\)-adic aspects of Jacobi forms, Arithmétique des courbes elliptiques à réduction supersingulière enp, The radius of convergence of the \(p\)-adic sigma function, On 3-adic heights on elliptic curves, The work of Barry Mazur, On the universal \(p\)-adic sigma and Weierstrass zeta functions, Quadratic Chabauty for (bi)elliptic curves and Kim's conjecture, Elliptic nets and elliptic curves, Jacobi forms and \(p\)-adic Weber formula, A higher-order generalization of Jacobi's derivative formula and its algebraic geometric analogue, Iwasawa theory and \(p\)-adic heights, Resultants and discriminants of multiplication polynomials for elliptic curves, Prime power terms in elliptic divisibility sequences, Universal norms on abelian varieties over global function fields, Algebraic theta functions and the \(p\)-adic interpolation of Eisenstein-Kronecker numbers, \(p\)-adic properties of division polynomials and elliptic divisibility sequences, Efficient Computation of p-Adic Heights, Arithmetical Power Series Expansion of the Sigma Function for a Plane Curve, Algorithms for the arithmetic of elliptic curves using Iwasawa theory, $p$-adic heights of Heegner points and $\Lambda $-adic regulators, Honda-Kaneko congruences and the Mazur-Tate \(p\)-adic \(\sigma\)-function, Overview of Some Iwasawa Theory

Cites Work

• Fonctions thêta et théorème du cube
• Infinite descent and \(p\)-adic heights over elliptic curves with complex multiplication
• On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• The arithmetic of elliptic curves
• The crystals associated to Barsotti-Tate groups: with applications to Abelian schemes
• P-Adic Theta Functions
• Hauteurs et fonctions thêta
• Theta Functions and Abelian Varieties over Valuation Fields of Rank one I
• On Theta Functions and Abelian Varieties over Valuation Fields of Rank One: (II) Theta Functions and Abelian Functions of Characteristicp(>0)
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