Connections between for even quadratic Dirichlet characters and class numbers of appropriate imaginary quadratic fields, II
Connections between for even quadratic Dirichlet characters and class numbers of appropriate imaginary quadratic fields, I
Connections between binary patterns and paperfolding
Connections between connected topological spaces on the set of positive integers
In this paper we introduce a connected topology T on the set ℕ of positive integers whose base consists of all arithmetic progressions connected in Golomb’s topology. It turns out that all arithmetic progressions which are connected in the topology T form a basis for Golomb’s topology. Further we examine connectedness of arithmetic progressions in the division topology T′ on ℕ which was defined by Rizza in 1993. Immediate consequences of these studies are results concerning local connectedness of...
Consecutive evaluation of Euler sums.
Consecutive integers in algebraic number fields.
Consecutive powers in continued fractions
Consecutive primes in tuples
In a stunning new advance towards the Prime k-Tuple Conjecture, Maynard and Tao have shown that if k is sufficiently large in terms of m, then for an admissible k-tuple of linear forms in ℤ[x], the set contains at least m primes for infinitely many n ∈ ℕ. In this note, we deduce that contains at least m consecutive primes for infinitely many n ∈ ℕ. We answer an old question of Erdős and Turán by producing strings of m + 1 consecutive primes whose successive gaps form an increasing (resp....
Consequences of a theorem of Erdős-Prachar.
Conservative polynomials and yet another action of on plane trees
In this paper we study an action of the absolute Galois group on bicolored plane trees. In distinction with the similar action provided by the Grothendieck theory of “Dessins d’enfants” the action is induced by the action of on equivalence classes of conservative polynomials which are the simplest examples of postcritically finite rational functions. We establish some basic properties of the action and compare it with the Grothendieck action.
Conservative Quadratic Forms.
Considérations nouvelles sur le déterminant de Smith et Mansion
Constante de Lenstra et corps de nombres euclidiens
Constants for lower bounds for linear forms in the logarithms of algebraic numbers II. The homogeneous rational case
Constants for lower bounds for linear forms in the logarithms of algebraic numbers I. The general case
Constrained and generalized barycentric Davenport constants.
Constrained optimal control. The algebraic approach
Constructing an automorphic form from the orbit of a transformation.
Constructing class fields over local fields
Let be a -adic field. We give an explicit characterization of the abelian extensions of of degree by relating the coefficients of the generating polynomials of extensions of degree to the exponents of generators of the norm group . This is applied in an algorithm for the construction of class fields of degree , which yields an algorithm for the computation of class fields in general.
Constructing elliptic curves over finite fields using double eta-quotients
We examine a class of modular functions for whose values generate ring class fields of imaginary quadratic orders. This fact leads to a new algorithm for constructing elliptic curves with complex multiplication. The difficulties arising when the genus of is not zero are overcome by computing certain modular polynomials.Being a product of four -functions, the proposed modular functions can be viewed as a natural generalisation of the functions examined by Weber and usually employed to construct...