scholarly journals On the Generalized Brauer–Siegel Theorem for Asymptotically Exact Families of Number Fields with Solvable Galois Closure

2019 ◽  
Author(s):  
Anup B Dixit
Keyword(s):  
Number Fields ◽  
Galois Closure ◽  
Siegel Theorem

Abstract In 2002, M. A. Tsfasman and S. G. Vlăduţ formulated the generalized Brauer–Siegel conjecture for asymptotically exact families of number fields. In this article, we establish this conjecture for asymptotically good towers and asymptotically bad families of number fields with solvable Galois closure.

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 $L\in \mathcal {C}$ .

scholarly journals ON LOGARITHMIC DERIVATIVES OF ZETA FUNCTIONS IN FAMILIES OF GLOBAL FIELDS

2011 ◽  
Vol 07 (08) ◽  
pp. 2139-2156 ◽  
Author(s):  
PHILIPPE LEBACQUE ◽  
ALEXEY ZYKIN
Keyword(s):  
Error Term ◽  
Function Fields ◽  
Zeta Functions ◽  
Number Fields ◽  
Global Fields ◽  
And Function ◽  
Derivatives Of ◽  
Logarithmic Derivatives ◽  
Siegel Theorem

We prove a formula for the limit of logarithmic derivatives of zeta functions in families of global fields with an explicit error term. This can be regarded as a rather far reaching generalization of the explicit Brauer–Siegel theorem both for number fields and function fields.

scholarly journals Cutting towers of number fields

2021 ◽  
Author(s):  
Farshid Hajir ◽  
Christian Maire ◽  
Ravi Ramakrishna
Keyword(s):  
Number Fields

scholarly journals Theta series and number fields: theorems and experiments

2021 ◽  
Author(s):  
Adrian Barquero-Sanchez ◽  
Guillermo Mantilla-Soler ◽  
Nathan C. Ryan
Keyword(s):  
Theta Series ◽  
Number Fields

Kummer theory for number fields via entanglement groups

2021 ◽  
Author(s):  
Antonella Perucca ◽  
Pietro Sgobba ◽  
Sebastiano Tronto
Keyword(s):  
Number Fields ◽  
Kummer Theory

scholarly journals Hyperbolic tessellations and generators of for imaginary quadratic fields

2021 ◽  
Vol 9 ◽  
Author(s):  
David Burns ◽  
Rob de Jeu ◽  
Herbert Gangl ◽  
Alexander D. Rahm ◽  
Dan Yasaki
Keyword(s):  
Number Field ◽  
Number Fields ◽  
Quadratic Fields ◽  
Quadratic Number ◽  
Imaginary Quadratic Fields ◽  
Quadratic Number Fields ◽  
Formula Group ◽  
Imaginary Quadratic Number ◽  
Direct Calculations

Abstract We develop methods for constructing explicit generators, modulo torsion, of the $K_3$ -groups of imaginary quadratic number fields. These methods are based on either tessellations of hyperbolic $3$ -space or on direct calculations in suitable pre-Bloch groups and lead to the very first proven examples of explicit generators, modulo torsion, of any infinite $K_3$ -group of a number field. As part of this approach, we make several improvements to the theory of Bloch groups for $ K_3 $ of any field, predict the precise power of $2$ that should occur in the Lichtenbaum conjecture at $ -1 $ and prove that this prediction is valid for all abelian number fields.

scholarly journals The 2-rank of the class group of some real cyclic quartic number fields

2021 ◽  
Vol 131 (1) ◽  
Author(s):  
Abdelmalek Azizi ◽  
Mohammed Tamimi ◽  
Abdelkader Zekhnini
Keyword(s):  
Class Group ◽  
Number Fields
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