Add to ORKGFix a totally real number field F of degree at least 2. Under the assumptions of the generalized Riemann hypothesis and Artin\u27s conjecture on the entirety of Artin L-functions, we derive an upper bound (in terms of the discriminant) on the class number of any CM number field with maximal real subfield F. This bound is a refinement of a bound established by Duke in 2001. Under the same hypotheses, we go on to prove that there exist infinitely many CM-extensions of F whose class numbers essentially meet this improved bound and whose Galois groups are as large as possible
AbstractEmploying a technique introduced by Gallagher, a simple derivation is given of Montgomery's ...
Abstract. We give explicit upper bounds for the discriminants of the non-normal quartic CM-fields wi...
International audienceIn this article we extend the main result of F. Amoroso and R. Dvornicich ``A ...
Fix a totally real number field F of degree at least 2. Under the assumptions of the generalized Rie...
Assuming the Generalized Riemann Hypothesis (GRH) and the Artin conjecture for Artin L-functions, Du...
The determination of the class number of totally real fields of large discriminant is known to be a ...
This paper is a continuation of [2]. We construct unconditionally several families of number fields ...
AbstractHere, we construct infinitely many number fields of any given degree d>1 whose class numbers...
AbstractIt is known that if we assume the Generalized Riemann Hypothesis, then any normal CM-field w...
AbstractFor a prime numberl, leth+lbe the class number of the maximal real subfield of thel-th cyclo...
In this dissertation, we undertake the study of the class numbers of fields of bounded relative degr...
We prove an improvement on Schmidt's upper bound on the number of number fields of degree $n$ and ab...
AbstractIn the first part of the paper we show how to construct real cyclotomic fields with large cl...
Assuming Generalized Riemann's Hypothesis, Bach proved that the class group SICK of a number field K...
AbstractThe aim of this paper is to give new upper bounds for Euclidean minima of algebraic number f...
AbstractEmploying a technique introduced by Gallagher, a simple derivation is given of Montgomery's ...
Abstract. We give explicit upper bounds for the discriminants of the non-normal quartic CM-fields wi...
International audienceIn this article we extend the main result of F. Amoroso and R. Dvornicich ``A ...
Fix a totally real number field F of degree at least 2. Under the assumptions of the generalized Rie...
Assuming the Generalized Riemann Hypothesis (GRH) and the Artin conjecture for Artin L-functions, Du...
The determination of the class number of totally real fields of large discriminant is known to be a ...
This paper is a continuation of [2]. We construct unconditionally several families of number fields ...
AbstractHere, we construct infinitely many number fields of any given degree d>1 whose class numbers...
AbstractIt is known that if we assume the Generalized Riemann Hypothesis, then any normal CM-field w...
AbstractFor a prime numberl, leth+lbe the class number of the maximal real subfield of thel-th cyclo...
In this dissertation, we undertake the study of the class numbers of fields of bounded relative degr...
We prove an improvement on Schmidt's upper bound on the number of number fields of degree $n$ and ab...
AbstractIn the first part of the paper we show how to construct real cyclotomic fields with large cl...
Assuming Generalized Riemann's Hypothesis, Bach proved that the class group SICK of a number field K...
AbstractThe aim of this paper is to give new upper bounds for Euclidean minima of algebraic number f...
AbstractEmploying a technique introduced by Gallagher, a simple derivation is given of Montgomery's ...
Abstract. We give explicit upper bounds for the discriminants of the non-normal quartic CM-fields wi...
International audienceIn this article we extend the main result of F. Amoroso and R. Dvornicich ``A ...