Fast computation of Gauss sums and resolution of the root of unity ambiguity
Faster algorithms for Frobenius numbers.
Faster and faster convergent series for .
Finding the eigenvalue in Elkies' algorithm.
Fonction sommatoire de la fonction de Möbius, 3. Majorations asymptotiques effectives fortes
On établit les majorations , valable pour qui est la meilleure majoration possible en valable pour tout , et d’autres analogues. On montre enfin comment trouver des majorations effectives pour tout .
From explicit estimates for primes to explicit estimates for the Möbius function
Fundamental units in a family of cubic fields
Let be the maximal order of the cubic field generated by a zero of for , . We prove that is a fundamental pair of units for , if
Further results on derived sequences.
Généralisation d'une famille de Shanks
Generalization of the formula of Faa di Bruno for a composite function with a vector argument.
Generalized perfect numbers.
Generalized Staircases: Recurrence and Symmetry
We study infinite translation surfaces which are -covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.
GiANT: Graphical Algebraic Number Theory
While most algebra is done by writing text and formulas, diagrams have always been used to present structural information clearly and concisely. Text shells are the de facto interface for computational algebraic number theory, but they are incapable of presenting structural information graphically. We present GiANT, a newly developed graphical interface for working with number fields. GiANT offers interactive diagrams, drag-and-drop functionality, and typeset formulas.
Hierarchical residue number systems with small moduli and simple converters
In this paper, a new class of Hierarchical Residue Number Systems (HRNSs) is proposed, where the numbers are represented as a set of residues modulo factors of 2k ± 1 and modulo 2k . The converters between the proposed HRNS and the positional binary number system can be built as 2-level structures using efficient circuits designed for the RNS (2k-1, 2k, 2k+1). This approach allows using many small moduli in arithmetic channels without large conversion overhead. The advantages resulting from the...
Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields
We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a -adic factorization method based on Newton polygons of higher order. The running-time and memory requirements of the algorithm appear to be very good.
Historia de las fórmulas y algoritmos para n.
How to compute the coefficients of the elliptic modular function .
How to explicitly solve a Thue-Mahler equation
Hurwitz and Tasoev continued fractions with long period.
Hyper-sums of powers of integers and the Akiyama-Tanigawa matrix.