O Fermatových číslech
Odometers and Toeplitz systems revisited in the context of Sarnak's conjecture
Although Sarnak's conjecture holds for compact group rotations (irrational rotations, odometers), it is not even known whether it holds for all Jewett-Krieger models of such rotations. In this paper we show that it does, as long as the model is at the same a topological extension, via the same map that establishes the isomorphism, of an equicontinuous model. In particular, we recover (after [AKL]) that regular Toeplitz systems satisfy Sarnak's conjecture, and, as another consequence, so do...
On a compositeness test for .
On a generalization of the Narayana triangle.
On a number pyramid related to the binomial, Deleham, Eulerian, MacMahon and Stirling number triangles.
On a number theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman–De Bruijn function
It is well known that getting the estimate of integral points in right-angled simplices is equivalent to getting the estimate of Dickman-De Bruijn function which is the number of positive integers and free of prime factors . Motivating from the Yau Geometry Conjecture, the third author formulated the Number Theoretic Conjecture which gives a sharp polynomial upper estimate that counts the number of positive integral points in n-dimensional () real right-angled simplices. In this paper, we...
On a sequence arising in algebraic geometry.
On computing Belyi maps
We survey methods to compute three-point branched covers of the projective line, also known as Belyĭ maps. These methods include a direct approach, involving the solution of a system of polynomial equations, as well as complex analytic methods, modular forms methods, and -adic methods. Along the way, we pose several questions and provide numerous examples.
On computing subfields. A detailed description of the algorithm
Let be an algebraic number field given by the minimal polynomial of . We want to determine all subfields of given degree. It is convenient to describe each subfield by a pair such that is the minimal polynomial of . There is a bijection between the block systems of the Galois group of and the subfields of . These block systems are computed using cyclic subgroups of the Galois group which we get from the Dedekind criterion. When a block system is known we compute the corresponding...
On consecutive integer pairs with the same sum of distinct prime divisors.
On cyclotomic polynomials with coefficients.
On Elkies subgroups of -torsion points in elliptic curves defined over a finite field
As a subproduct of the Schoof-Elkies-Atkin algorithm to count points on elliptic curves defined over finite fields of characteristic , there exists an algorithm that computes, for an Elkies prime, -torsion points in an extension of degree at cost bit operations in the favorable case where .We combine in this work a fast algorithm for computing isogenies due to Bostan, Morain, Salvy and Schost with the -adic approach followed by Joux and Lercier to get an algorithm valid without any limitation...
On elliptic diophantine equations that defy Thue's method: The case of the Ochoa curve.
On evaluations of infinite double sums and Tornheim's double series.
On Factor Tables, with an Account of the Mode of Formation of the Factor Table for the Fourth Million [Book]
On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function.
On integer sequences associated with the cyclic and complete graphs.
On integers of the form
On normal integral bases in ray class fields over imaginary quadratic fields
On power values of pyramidal numbers, I