scientific article; zbMATH DE number 706265

Publication date: 1 January 1995

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

modular functions complex multiplication elliptic functions canonical height $L$-series minimal model $p$-adic uniformization Mordell-Weil theorem for function fields Néron-model

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Elliptic curves (14H52) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Elliptic curves over local fields (11G07) Arithmetic algebraic geometry (Diophantine geometry) (11Gxx)

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statistical view on the conjecture of Lang about the canonical height on elliptic curves, Unnamed Item, Generators and integral points on twists of the Fermat cubic, Local invariants of isogenous elliptic curves, An analogue of the Washington-Sinnott theorem for elliptic curves with complex multiplication I, Periods of ordinary abelian varieties in characteristic p, Wiles defect for Hecke algebras that are not complete intersections, The Mordell-Weil bases for the elliptic curve $y^2=x^3-m^2x+m^2$, Computing rational points on rank 1 elliptic curves via $L$-series and canonical heights, Integral points on elliptic curves over function fields of positive characteristic, Power operations in elliptic cohomology and representations of loop groups, The undecidability of cyclotomic towers, Computing canonical heights on the projective line with no factorization, On the Liouville function on rational polynomial values, Pursuing polynomial bounds on torsion, Classics revisited: Éléments de géométrie algébrique, Class numbers of $p$-groups of a given order., Using elliptic curves to produce quadratic number fields of high three-rank, Three-descent and the Birch and Swinnerton-Dyer conjecture, Néron models, Lie algebras, and reduction of curves of genus one, Quantum lattice enumeration and tweaking discrete pruning, Form class groups for extended ring class fields, A family of monogenic $S_4$ quartic fields arising from elliptic curves, Evaluation of certain hypergeometric functions over finite fields, Sequences of fields with many solutions to the unit equation, On an elliptic analogue of Zagier's conjecture, Some coverings defined over $\mathbb{Q}$, Highly ramified pencils of elliptic curves in characteristic 2, Root numbers and algebraic points on elliptic surfaces with base $\mathbb{P}^1$, Triangles and elliptic curves. VI, Analogue of the Brauer-Siegel theorem for Legendre elliptic curves, Torsion subgroups of elliptic curves over quadratic cyclotomic fields in elementary abelian 2-extensions, Rational points on algebraic curves that change genus, On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields, Remarks on mod-$l^n$ representations, $l=3,5$, On the cyclic torsion of elliptic curves over cubic number fields, Néron models, On Mordell-Weil groups and congruences between derivatives of twisted Hasse-Weil $L$-functions, Eisenstein series and their applications to some arithmetic identities and congruences, Weierstrass equations for Jacobian fibrations on a certain $K3$ surface, Siegel's theorem and the Shafarevich conjecture, Lehmer's conjecture for polynomials satisfying a congruence divisibility condition and an analogue for elliptic curves, Complex multiplication symmetry of black hole attractors, The $p$-adic Gross-Zagier formula for elliptic curves at supersingular primes, On the rank of elliptic curves coming from rational Diophantine triples, Torsion in the cohomology of desingularized fiber products of elliptic surfaces, When is a polygonal pyramid number again polygonal?, Congruence formulas for Legendre modular polynomials, Towards practical key exchange from ordinary isogeny graphs, Variation of the reduction type of elliptic curves under small base change with wild ramification, On the distribution of congruent numbers, A lower bound for the canonical height on elliptic curves over abelian extensions., Ramification in the division fields of an elliptic curve, Integral points in arithmetic progression on $y^2= x(x^2-n^2)$, Root numbers and algebraic points on elliptic surfaces with elliptic base, The space of rational maps on $\mathbf P^1$, Elliptic curve lifting problem and its applications, A simple proof of a theorem of Parish, String-theory realization of modular forms for elliptic curves with complex multiplication, Langlands reciprocity for $C^\ast $-algebras, The greatest common valuation of $\phi_n$ and $\psi_n^2$ at points on elliptic curves, There are genus one curves of every index over every infinite, finitely generated field, Elliptic curves with torsion groups $\mathbb{Z}/8\mathbb{Z}$ and $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/6\mathbb{Z}$, Generalised pairs in birational geometry, Galois groups in a family of dynatomic polynomials, Elliptically distributed lozenge tilings of a hexagon, Moduli interpretations for noncongruence modular curves, On oriented supersingular elliptic curves, Path planning with objectives minimum length and maximum clearance, Elliptic curves containing sequences of consecutive cubes, On Ceva points of (almost) equilateral triangles, Bounds on special values of $L$-functions of elliptic curves in an Artin-Schreier family, The classification of purely non-symplectic automorphisms of high order on $K3$ surfaces, The Fermat equation over $\mathbb Q(\sqrt 2)$, An elliptic curve test for Mersenne primes, Uniform bounds on the number of rational points of a family of curves of genus 2, $p$-adic properties of division polynomials and elliptic divisibility sequences, A quantitative primitive divisor result for points on elliptic curves, Special arithmetic of flavor, On the Birch-Swinnerton-Dyer quotients modulo squares, A non-abelian conjecture of Tate-Shafarevich type for hyperbolic curves, A note on elliptic curves with a rational 3-torsion point, Algebraic approaches for solving isogeny problems of prime power degrees, Arithmetic partial differential equations. I, Generalized Birch lemma and the 2-part of the Birch and Swinnerton-Dyer conjecture for certain elliptic curves, Primitive divisors of sequences associated to elliptic curves with complex multiplication, Computing special $L$-values of certain modular forms with complex multiplication, Explicit Heegner points: Kolyvagin's conjecture and non-trivial elements in the Shafarevich-Tate group, Arithmetic of a singular $K3$ surface, On higher fitting ideals of certain Iwasawa modules associated with Galois representations and Euler systems, Torsion free sheaves on Weierstrass cubic curves and the classical Yang-Baxter equation, Speeding up Huff form of elliptic curves, Reducible mod 105 representations and modularity of elliptic curves, Acyclotomy of torsion in the CM case, On singular moduli that are $S$-units, Construction of high rank elliptic curves, Isogenies of degree $p$ of elliptic curves over local fields and Kummer theory., Measuring the height of a polynomial, Expander graphs based on GRH with an application to elliptic curve cryptography, The Witt ring of an elliptic curve over a local field, Galois graphs: Walks, trees and automorphisms, Modular forms arising from divisor functions, Paramodular forms coming from elliptic curves, The geometry of the third moment of exponential sums, Good reduction of elliptic curves over imaginary quadratic fields, Point counting on reductions of CM elliptic curves, On the product of twists of rank two and a conjecture of Larsen, Rank of $K_2$ of elliptic curves, 5-torsion in the Shafarevich-Tate group of a family of elliptic curves, On the $p$-adic realization of elliptic polylogarithms for CM-elliptic curves, Odd power divisor functions in positive characteristic, Potential good reduction of elliptic curves., Measures of simultaneous approximation for quasi-periods of Abelian varieties, The Cassels-Tate pairing and the Platonic solids.