Prime divisors of Lucas sequences
Prime factorization of integral Cayley octaves
Prime factors of class number of cyclotomic fields
Let be an odd prime, be a primitive root modulo and with . In 2007, R. Queme raised the question whether the -rank ( an odd prime ) of the ideal class group of the -th cyclotomic field is equal to the degree of the greatest common divisor over the finite field of and Kummer’s polynomial . In this paper, we shall give the complete answer for this question enumerating a counter-example.
Prime factors of values of polynomials
We prove that for every quadratic binomial f(x) = rx² + s ∈ ℤ[x] there are pairs ⟨a,b⟩ ∈ ℕ² such that a ≠ b, f(a) and f(b) have the same prime factors and min{a,b} is arbitrarily large. We prove the same result for every monic quadratic trinomial over ℤ.
Prime Ideal Decomposition in F (...).
Prime producing polynomials: Proof of a conjecture by Mollin and Williams
Prime valued polynomials and class numbers of quadratic fields.
Prime values of irreducible polynomials
Primes, permutations and primitive roots.
Primes which remain irreducible in a normal field
Primitive divisors of the expression An - Bn in algebraic number fields.
Primitive elements in integral bases
Principalization algorithm via class group structure
For an algebraic number field with -class group of type , the structure of the -class groups of the four unramified cyclic cubic extension fields , , of is calculated with the aid of presentations for the metabelian Galois group of the second Hilbert -class field of . In the case of a quadratic base field it is shown that the structure of the -class groups of the four -fields frequently determines the type of principalization of the -class group of in . This provides...
Principe d’Heisenberg et fonctions positives
On décrit un problème naturel concernant la transformation de Fourier. Soient , deux fonctions associées par celle-ci, positives pour et nulles en zéro. Quelle est la borne inférieure pour ? En dimension supérieure, même question, l’intervalle étant remplacé par la boule de rayon . On montre l’existence d’une borne inférieure strictement positive, qui est estimée en fonction de la dimension. La dernière section montre que cette question est naturellement liée à la théorie des fonctions zêta....
Problèmes de construction en multiplication complexe
Problèmes de nombres de classes de corps quadratiques imaginaires
Problèmes de normes dans les extensions galoisiennes de corps de nombres.
Problèmes relatifs aux -classes d’idéaux dans les extensions cycliques relatives de degré premier
Products in K-theory and Intersecting Algebraic Cycles.
Prolongement analytique et valeurs aux entiers négatifs de certaines sacute;ries arithmétiques relatives à des formes quadratiques.