EuDML | Browse

Let $C$ be a hyperelliptic curve of genus $g \geq 1$ over a number field $K$ with good reduction outside a finite set of places $S$ of $K$ . We prove that $C$ has a Weierstrass model over the ring of integers of $K$ with height effectively bounded only in terms of $g$ , $S$ and $K$ . In particular, we obtain that for any given number field $K$ , finite set of places $S$ of $K$ and integer $g \geq 1$ one can in principle determine the set of $K$ -isomorphism classes of hyperelliptic curves over $K$ of genus $g$ with good reduction outside $S$ .

An effective result of André-Oort type II

Lars Kühne (2013)

Acta Arithmetica

We prove some new effective results of André-Oort type. In particular, we state certain uniform improvements of the main result in [L. Kühne, Ann. of Math. 176 (2012), 651-671]. We also show that the equation X + Y = 1 has no solution in singular moduli. As a by-product, we indicate a simple trick rendering André's proof of the André-Oort conjecture effective. A significantly new aspect is the usage of both the Siegel-Tatuzawa theorem and the weak effective lower bound on the class number of an...

An effective Shafarevich theorem for elliptic curves

Clemens Fuchs, Rafael von Känel, Gisbert Wüstholz (2011)

Acta Arithmetica

An effective solution of a certain diophantine problem

U. Zannier (1995)

Rendiconti del Seminario Matematico della Università di Padova

An effective Version of Faltings' Product Theorem.

Roberto Ferretti (1996)

Forum mathematicum

An Egyptian algorithm for polynomials.

D.E. Dobbs, R.M. McConnel (1984)

Elemente der Mathematik

An Elementary Approach to Hecke Operators.

Erik Lippa (1973)

Mathematische Annalen

An elementary identity in the theory of Hecke L-functions.

Uwe Weselmann (1989)

Inventiones mathematicae

An elementary method in prime number theory

R. Vaughan (1980)

Acta Arithmetica

An elementary proof of a congruence by Skula and Granville

Romeo Meštrović (2012)

Archivum Mathematicum

Let $p \geq 5$ be a prime, and let $q_{p} (2) : = (2^{p - 1} - 1) / p$ be the Fermat quotient of $p$ to base $2$ . The following curious congruence was conjectured by L. Skula and proved by A. Granville $q_{p} {(2)}^{2} \equiv - \sum_{k = 1}^{p - 1} \frac{2^{k}}{k^{2}} (mod p) .$ In this note we establish the above congruence by entirely elementary number theory arguments.

An elementary proof of the Davenport-Hasse relation

Stanislav Jakubec (2001)

Mathematica Slovaca

An elementary proof of the Mazur-Tate-Teitelbaum conjecture for elliptic curves.

Kobayashi, Shinichi (2007)

Documenta Mathematica

An elementary proof that almost all real numbers are normal.

Filip, Ferdinánd, Šustek, Jan (2010)

Acta Universitatis Sapientiae. Mathematica

An elementary treatment of a general diophantine problem

Nigel Watt (1988)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

An elliptic analogue of the Franklin-Schneider theorem

Alex Bijlsma (1980)

Annales de la Faculté des sciences de Toulouse : Mathématiques

An elliptic analogue of the multiple Dedekind sums

Shigeki Egami (1995)

Compositio Mathematica

An elliptic curve having large integral points

Yanfeng He, Wenpeng Zhang (2010)

Czechoslovak Mathematical Journal

The main purpose of this paper is to prove that the elliptic curve $E : y^{2} = x^{3} + 27 x - 62$ has only the integral points $(x, y) = (2, 0)$ and $(28844402, \pm 154914585540)$ , using elementary number theory methods and some known results on quadratic and quartic Diophantine equations.

Currently displaying 1401 – 1420 of 16591

Previous Page 71 Next