scholarly journals Stark's conjecture in multi-quadratic extensions, revisited

2003 ◽  
Vol 15 (1) ◽  
pp. 83-97 ◽  
Author(s):  
David S. Dummit ◽  
Jonathan W. Sands ◽  
Brett Tangedal
Keyword(s):  
Quadratic Extensions ◽  
Stark's Conjecture

ON HIGHER-ORDER STICKELBERGER-TYPE THEOREMS FOR MULTI-QUADRATIC EXTENSIONS

2012 ◽  
Vol 08 (01) ◽  
pp. 95-110 ◽  
Author(s):  
DANIEL MACIAS CASTILLO
Keyword(s):  
Higher Order ◽  
Ideal Class ◽  
Quadratic Extensions ◽  
Galois Modules ◽  
Ideal Class Groups ◽  
Stark's Conjecture ◽  
Wide Range ◽  
Tamagawa Number Conjecture ◽  
Derivatives Of ◽  
Integral Version

We prove, for all quadratic and a wide range of multi-quadratic extensions of global fields, a result concerning the annihilation as Galois modules of ideal class groups by explicit elements constructed from the values of higher-order derivatives of Dirichlet L-functions. This result simultaneously refines Rubin's integral version of Stark's Conjecture and provides evidence for the relevant case of the Equivariant Tamagawa Number Conjecture of Burns and Flach.

Power Integral Bases in Composits of Number Fields

1998 ◽  
Vol 41 (2) ◽  
pp. 158-165 ◽  
Author(s):  
István Gaál
Keyword(s):  
Number Fields ◽  
Parametric Family ◽  
Prime Degree ◽  
Index Form ◽  
Form Equation ◽  
Integral Bases ◽  
Quadratic Extensions ◽  
Totally Real

AbstractIn the present paper we consider the problem of finding power integral bases in number fields which are composits of two subfields with coprime discriminants. Especially, we consider imaginary quadratic extensions of totally real cyclic number fields of prime degree. As an example we solve the index form equation completely in a two parametric family of fields of degree 10 of this type.

scholarly journals Combinatorics on Finite Fields: the Sign Repartition for the Quadratic Residues

2014 ◽  
Vol 22 (1) ◽  
pp. 41-44
Author(s):  
Şerban Bărcănescu
Keyword(s):  
Finite Fields ◽  
Class Number ◽  
Quadratic Extensions ◽  
Quadratic Residues

AbstractIn the present paper we present the equivalence between the combinatorial determination of the sign repartition for the quadratic residues and non-residues to the computation of the class number of certain quadratic extensions of the field of rationals.

ON STARK’S CLASS NUMBER CONJECTURE AND THE GENERALISED BRAUER–SIEGEL CONJECTURE

2022 ◽  
pp. 1-13
Author(s):  
PENG-JIE WONG
Keyword(s):  
Class Number ◽  
Number Fields ◽  
Galois Closure ◽  
Stark's Conjecture

Abstract Stark conjectured that for any $h\in \Bbb {N}$ , there are only finitely many CM-fields with class number h. Let $\mathcal {C}$ be the class of number fields L for which L has an almost normal subfield K such that $L/K$ has solvable Galois closure. We prove Stark’s conjecture for $L\in \mathcal {C}$ of degree greater than or equal to 6. Moreover, we show that the generalised Brauer–Siegel conjecture is true for asymptotically good towers of number fields $L\in \mathcal {C}$ and asymptotically bad families of $L\in \mathcal {C}$ .

On an Exceptional Phenomenon in Certain Quadratic Extensions

1954 ◽  
Vol 6 ◽  
pp. 474-476 ◽  
Author(s):  
H. B. Mann
Keyword(s):  
Cyclic Extension ◽  
Quadratic Extensions ◽  
Image Position

Let Ω be a cyclic extension of degree l over the field Σ. Correcting an error which for some time had been haunting the literature, Hasse (1, p. 272) noted that for l = 2, the field Ω may contain a unit ξ such that.

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