Chebyshev's bias.
Chebyshev's method for number fields
We give an elementary proof of an explicit estimate for the number of primes splitting completely in an extension of the rationals. The proof uses binomial coefficents and extends Chebyshev's classical approach.
Chen's double sieve, Goldbach's conjecture and the twin prime problem, 2
Chen's double sieve, Goldbach's conjecture and the twin prime problem
Chen's theorem in short intervals
Chen's theorem in totally real algebraic number fields
Circles passing through five or more integer points
We find an improvement to Huxley and Konyagin’s current lower bound for the number of circles passing through five integer points. We conjecture that the improved lower bound is the asymptotic formula for the number of circles passing through five integer points. We generalise the result to circles passing through more than five integer points, giving the main theorem in terms of cyclic polygons with m integer point vertices. Theorem. Let m ≥ 4 be a fixed integer. Let be the number of cyclic polygons...
Class Number Two for Real Quadratic Fields of Richaud-Degert Type
2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.This paper contains proofs of conjectures made in [16] on class number 2 and what this author has dubbed the Euler-Rabinowitsch polynomial for real quadratic fields. As well, we complete the list of Richaud-Degert types given in [16] and show how the behaviour of the Euler-Rabinowitsch polynomials and certain continued fraction expansions come into play in the complete determination...
Class numbers of elliptic function fields and the distribution of prime numbers
Closed orbits of -extension of ergodic toral automorphisms.
Coincidences in the values of the Euler and Carmichael functions
Combinatoire du billard dans un polyèdre
Ces notes ont pour but de rassembler les différents résultats de combinatoire des mots relatifs au billard polygonal et polyédral. On commence par rappeler quelques notions de combinatoire, puis on définit le billard, les notions utiles en dynamique et le codage de l’application. On énonce alors les résultats connus en dimension deux puis trois.
Compact integers and factorials
Comparing the number of abelian groups and of semisimple rings of a given order
Completely q-multiplicative functions: the Mellin transform approach
Comportement asymptotique du produit des k premiers nombres premiers généralisés
Comportement des fonctions arithmétiques complexes, multiplicatives, à valeurs dans le disque
Comportement Moyen du Cardinal de Certains Ensembles de Facteurs Premiers.
Composite positive integers whose sum of prime factors is prime
In this note, we show that the counting function of the number of composite positive integers such that is a prime is of order of magnitude at least and at most .
Composite positive integers with an average prime factor