Computing all elements of given index in sextic fields with a cubic subfield
Computing all monogeneous mixed dihedral quartic extensions of a quadratic field
Let be a given real quadratic field. We give a fast algorithm for determining all dihedral quartic fields with mixed signature having power integral bases and containing as a subfield. We also determine all generators of power integral bases in . Our algorithm combines a recent result of Kable [9] with the algorithm of Gaál, Pethö and Pohst [6], [7]. To illustrate the method we performed computations for
Computing integral points on elliptic curves
Computing integral points on Mordell's elliptic curves.
Congruence and uniqueness of certain Markoff numbers
Congruence properties of the number of solutions of some equations.
Congruences with factorials modulo .
Congruent numbers over real number fields
It is classical that a natural number n is congruent iff the rank of ℚ -points on Eₙ: y² = x³-n²x is positive. In this paper, following Tada (2001), we consider generalised congruent numbers. We extend the above classical criterion to several infinite families of real number fields.
Congruent numbers with higher exponents
This paper investigates the system of equations in positive integers , , , , where and are positive integers with . In case of we would obtain the classical problem of congruent numbers. We provide a procedure to solve the simultaneous equations above for a class of the coefficient with the condition . Further, under same condition, we even prove a finiteness theorem for arbitrary nonzero .
Constrained optimal control. The algebraic approach
Constructing fifteen infinite classes of nonregular bipartite integral graphs.
Construction d'une table de nombres congruents
Continued fractions of Laurent series with partial quotients from a given set
Contre-exemples au principe de Hasse pour certains tores coflasques
Nous étudions le comportement asymptotique du nombre de variétés dans une certaine classe ne satisfaisant pas le principe de Hasse. Cette étude repose sur des résultats récemment obtenus par Colliot-Thélène [3].
Contre-exemples au principe de Hasse pour les courbes de Fermat
Let p be an odd prime number. In this paper, we are concerned with the behaviour of Fermat curves defined over ℚ, given by equations , with respect to the local-global Hasse principle. It is conjectured that there exist infinitely many Fermat curves of exponent p which are counterexamples to the Hasse principle. This is a consequence of the abc-conjecture if p ≥ 5. Using a cyclotomic approach due to H. Cohen and Chebotarev’s density theorem, we obtain a partial result towards this conjecture, by...
Corps biquadratiques monogènes.
Corps de nombres algébriques d'anneau d'entiers monogène
Correction to: On Thue's equation. Invent. Math. 88, 69-81 (1987).
Corrections to "A quantitative version of Runge's theorem on diophantine equations" (Acta Arith. 62 (1992), 157-172)
Corrections to “How to explicitly solve a Thue-Mahler equation”