Add to ORKGIn this short note we confirm the relation between the generalized abc-conjecture and the p-rationality of number fields. Namely, we prove that given K{Q a real quadratic extension or an imaginary dihedral extension of degree 6, if the generalized abc-conjecture holds in K, then there exist at least c logX prime numbers p ď X for which K is p-rational, here c is some nonzero constant depending on K. The real quadratic case was recently suggested by Böckle-Guiraud-Kalyanswamy-Khare
integer a # * 1, or a perfect square, there exist infinitely many primes p for which a is a primiti...
This paper is the first in a series of four devoted to the abc conjecture, the Rie-mann Hypothesis, ...
In 2001, Stewart and Yu [1] proved that there exists effectively computable positive numbers c1 and ...
In this short note we confirm the relation between the generalized abc-conjecture and the p-rational...
Published in: Pub. Math. Besancon (Théorie des Nombres) (2019) (2), 29-51. https://pmb.centre-mersen...
In his work about Galois representations, Greenberg conjectured the existence, for any odd prime p a...
To appear in Publ. Math. Fac. Sci. Besançon (2019)New Sections and new applicationsLet K be a number...
For each prime p, we prove the existence of infinitely many real quadratic p-rational number fields ...
Pour chaque nombre premier p, nous prouvons l’existence d’une infinité de corps quadratiques réels p...
Note:This thesis examines the abc-conjecture, a conjectured diophantine inequality which makes a con...
International audienceIn this paper we make a series of numerical experiments to support Greenberg...
summary:Let $K/\mathbb {Q}$ be an algebraic number field of class number one and let $\mathcal {O}_K...
Weakened forms of the ABC conjecture are defined in terms of the upper k’th root functions. These we...
International audienceLet p be a prime number, and let K/k be a finite Galois extension of number fi...
Let $K\subseteq \mathbb{R}$ be a number field. Using techniques of discrete analysis, we prove that ...
integer a # * 1, or a perfect square, there exist infinitely many primes p for which a is a primiti...
This paper is the first in a series of four devoted to the abc conjecture, the Rie-mann Hypothesis, ...
In 2001, Stewart and Yu [1] proved that there exists effectively computable positive numbers c1 and ...
In this short note we confirm the relation between the generalized abc-conjecture and the p-rational...
Published in: Pub. Math. Besancon (Théorie des Nombres) (2019) (2), 29-51. https://pmb.centre-mersen...
In his work about Galois representations, Greenberg conjectured the existence, for any odd prime p a...
To appear in Publ. Math. Fac. Sci. Besançon (2019)New Sections and new applicationsLet K be a number...
For each prime p, we prove the existence of infinitely many real quadratic p-rational number fields ...
Pour chaque nombre premier p, nous prouvons l’existence d’une infinité de corps quadratiques réels p...
Note:This thesis examines the abc-conjecture, a conjectured diophantine inequality which makes a con...
International audienceIn this paper we make a series of numerical experiments to support Greenberg...
summary:Let $K/\mathbb {Q}$ be an algebraic number field of class number one and let $\mathcal {O}_K...
Weakened forms of the ABC conjecture are defined in terms of the upper k’th root functions. These we...
International audienceLet p be a prime number, and let K/k be a finite Galois extension of number fi...
Let $K\subseteq \mathbb{R}$ be a number field. Using techniques of discrete analysis, we prove that ...
integer a # * 1, or a perfect square, there exist infinitely many primes p for which a is a primiti...
This paper is the first in a series of four devoted to the abc conjecture, the Rie-mann Hypothesis, ...
In 2001, Stewart and Yu [1] proved that there exists effectively computable positive numbers c1 and ...