A functional equation originating from elliptic curves.
Displaying 21 – 40 of 1274
A fundamental domain for the Fermat curves and their quotients.
J. Guardia (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
A general framework for subexponential discrete logarithm algorithms
Andreas Enge, Pierrick Gaudry (2002)
Acta Arithmetica
A generalization of the Chowla-Selberg formula.
Y. Nakkajima, Y. Taguchi (1991)
Journal für die reine und angewandte Mathematik
A geometric proof of Kummer's reciprocity law for seventh powers
R. Clement Fernández, J. M. Echarri Hernández, E. J. Gómez Ayala (2011)
Acta Arithmetica
A Grunwald-Wang type theorem for abelian varieties
Brendan Creutz (2012)
Acta Arithmetica
A “Hardy-Littlewood” approach to the -unit equation
G. R. Everest (1989)
Compositio Mathematica
A local-global criterion for dynamics on ℙ¹
Joseph H. Silverman, José Felipe Voloch (2009)
Acta Arithmetica
A local-global principle for rational isogenies of prime degree
Andrew V. Sutherland (2012)
Journal de Théorie des Nombres de Bordeaux
Let be a number field. We consider a local-global principle for elliptic curves that admit (or do not admit) a rational isogeny of prime degree . For suitable (including ), we prove that this principle holds for all , and for , but find a counterexample when for an elliptic curve with -invariant . For we show that, up to isomorphism, this is the only counterexample.
A lower bound for the rank of
E. Kowalski, P. Michel (2000)
Acta Arithmetica
A moduli approach to quadratic -curves realizing projective mod Galois representations.
J. A. Fernández (2008)
Revista Matemática Iberoamericana
A motivic Chebotarev density theorem.
Dhillon, Ajneet, Mináč, Ján (2006)
The New York Journal of Mathematics [electronic only]
A natural series for the natural logarithm.
Dasbach, Oliver T. (2008)
The Electronic Journal of Combinatorics [electronic only]
A new record for the canonical height on an elliptic curve over .
Jain, Sonal (2010)
The New York Journal of Mathematics [electronic only]
A note on a paper of Franklin
D. Masser (1976)
Acta Arithmetica
A note on a product formula for the cubic Gauss sum
Hiroshi Ito (2012)
Acta Arithmetica
A note on arithmetic progressions on elliptic curves.
Campbell, Garikai (2003)
Journal of Integer Sequences [electronic only]
A note on arithmetic progressions on quartic elliptic curves.
Ulas, Maciej (2005)
Journal of Integer Sequences [electronic only]
A Note on heights in certain infinite extensions of
Enrico Bombieri, Umberto Zannier (2001)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
We study the behaviour of the absolute Weil height of algebraic numbers in certain infinite extensions of . In particular, we obtain a Northcott type property for infinite abelian extensions of finite exponent and also a Bogomolov type property for certain fields which are a -adic analog of totally real fields. Moreover, we obtain a non-archimedean analog of a uniform distribution theorem of Bilu in the archimedean case.
A note on integral points on elliptic curves
Mark Watkins (2006)
Journal de Théorie des Nombres de Bordeaux
We investigate a problem considered by Zagier and Elkies, of finding large integral points on elliptic curves. By writing down a generic polynomial solution and equating coefficients, we are led to suspect four extremal cases that still might have nondegenerate solutions. Each of these cases gives rise to a polynomial system of equations, the first being solved by Elkies in 1988 using the resultant methods of Macsyma, with there being a unique rational nondegenerate solution. For the second case...