The totally real extension of degree 6 with minimum discriminant.
The totally real extension of degree 6 with minimum discriminant.
The unitary amicable pairs to .
Thomas’ conjecture over function fields
Thomas’ conjecture is, given monic polynomials
Thue equations with composite fields
Topics in computational algebraic number theory
We describe practical algorithms from computational algebraic number theory, with applications to class field theory. These include basic arithmetic, approximation and uniformizers, discrete logarithms and computation of class fields. All algorithms have been implemented in the Pari/Gp system.
Totally indefinite Euclidean quaternion fields
We study the Euclidean property for totally indefinite quaternion fields. In particular, we establish a complete list of norm-Euclidean such fields over imaginary quadratic number fields. This enables us to exhibit an example which gives a negative answer to a question asked by Eichler. The proofs are both theoretical and algorithmic.
Transformation homographique appliquée à un développement en fraction continue fini ou infini
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.
Unisequences and nearest integer continued fraction midpoint criteria for Pell's equation.
Vacca-type series for values of the generalized Euler constant function and its derivative.
Verifying two conjectures on generalized elite primes.
Vyprávění o dvou sítech
Waring's problem for sixteen biquadrates. Numerical results
We explain the algorithms that we have implemented to show that all integers congruent to modulo in the interval are sums of five fourth powers, and that all integers congruent to or modulo in the interval are sums of seven fourth powers. We also give some results related to small sums of biquadrates. Combining with the Dickson ascent method, we deduce that all integers in the interval are sums of biquadrates.
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.
What is the inverse of repeated square and multiply algorithm?
It is well known that the repeated square and multiply algorithm is an efficient way of modular exponentiation. The obvious question to ask is if this algorithm has an inverse which would calculate the discrete logarithm and what is its time compexity. The technical hitch is in fixing the right sign of the square root and this is the heart of the discrete logarithm problem over finite fields of characteristic not equal to 2. In this paper a couple of probabilistic algorithms to compute the discrete...
Worst-case complexity, average-case complexity and lattice problems.
Young tableaux and other mutually describing sequences.
Алгоритм полиномиальной сложности для разложения многочленов и нахождение компонент многообразия в субэкспоненциальное время