Power integral bases in the family of simplest quartic fields.
Primitive divisors of Lucas and Lehmer sequences, II
Let and are conjugate complex algebraic integers which generate Lucas or Lehmer sequences. We present an algorithm to search for elements of such sequences which have no primitive divisors. We use this algorithm to prove that for all and with h, the -th element of these sequences has a primitive divisor for . In the course of proving this result, we give an improvement of a result of Stewart concerning more general sequences.
Rational products of sines of rational angles.
Solving conics over function fields
Let be a field whose characteristic is not and . We give a simple algorithm to find, given , a nontrivial solution in (if it exists) to the equation . The algorithm requires, in certain cases, the solution of a similar equation with coefficients in ; hence we obtain a recursive algorithm for solving diagonal conics over (using existing algorithms for such equations over ) and over .
Solving elliptic diophantine equations avoiding Thue equations and elliptic logarithms.
Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms. The case of quartic equations
Solving elliptic diophantine equations: the general cubic case
Sums of like powers and some dense sets.
Superelliptic Equations of the form y^p=x^kp+a_(kp-1)x^(kp-1)+...+a_0
The D(1)-extensions of D(-1)-triples 1,2,c and integer points on the attached elliptic curves
The Ljunggren equation revisited
We study the Ljunggren equation Y² + 1 = 2X⁴ using the "multiplication by 2" method of Chabauty.
The number Γ(k) in Waring's problem
Thomas’ conjecture over function fields
Thomas’ conjecture is, given monic polynomials
Thue equations with composite fields
Triangles with two integral sides.
Une courbe elliptique définie sur ℚ de rang ≥ 22
Nous présentons un exemple de courbe elliptique définie sur ℚ de rang ≥ 22 en détaillant les méthodes qui ont permis cette découverte.
Weighted Frobenius-Perron operators and their spectra
First, some classic properties of a weighted Frobenius-Perron operator on as a predual of weighted Koopman operator on will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of under certain conditions.