On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes

Stéphane Louboutin[1]

  • [1] Institut de Mathématiques de Luminy, UMR 6206 163, avenue de Luminy, Case 907 13288 Marseille Cedex 9, FRANCE

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 2, page 559-573
  • ISSN: 1246-7405

Abstract

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Lately, explicit upper bounds on | L ( 1 , χ ) | (for primitive Dirichlet characters χ ) taking into account the behaviors of χ on a given finite set of primes have been obtained. This yields explicit upper bounds on residues of Dedekind zeta functions of abelian number fields taking into account the behavior of small primes, and it as been explained how such bounds yield improvements on lower bounds of relative class numbers of CM-fields whose maximal totally real subfields are abelian. We present here some other applications of such bounds together with new bounds for non-abelian number fields.

How to cite

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Louboutin, Stéphane. "On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes." Journal de Théorie des Nombres de Bordeaux 17.2 (2005): 559-573. <http://eudml.org/doc/249456>.

@article{Louboutin2005,
abstract = {Lately, explicit upper bounds on $\vert L(1,\chi )\vert $ (for primitive Dirichlet characters $\chi $) taking into account the behaviors of $\chi $ on a given finite set of primes have been obtained. This yields explicit upper bounds on residues of Dedekind zeta functions of abelian number fields taking into account the behavior of small primes, and it as been explained how such bounds yield improvements on lower bounds of relative class numbers of CM-fields whose maximal totally real subfields are abelian. We present here some other applications of such bounds together with new bounds for non-abelian number fields.},
affiliation = {Institut de Mathématiques de Luminy, UMR 6206 163, avenue de Luminy, Case 907 13288 Marseille Cedex 9, FRANCE},
author = {Louboutin, Stéphane},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {$L$-functions; Dedekind zeta functions; number fields; class number; Class numbers; cubic and quartic extensions; cyclotomic fields; zeta functions},
language = {eng},
number = {2},
pages = {559-573},
publisher = {Université Bordeaux 1},
title = {On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes},
url = {http://eudml.org/doc/249456},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Louboutin, Stéphane
TI - On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 2
SP - 559
EP - 573
AB - Lately, explicit upper bounds on $\vert L(1,\chi )\vert $ (for primitive Dirichlet characters $\chi $) taking into account the behaviors of $\chi $ on a given finite set of primes have been obtained. This yields explicit upper bounds on residues of Dedekind zeta functions of abelian number fields taking into account the behavior of small primes, and it as been explained how such bounds yield improvements on lower bounds of relative class numbers of CM-fields whose maximal totally real subfields are abelian. We present here some other applications of such bounds together with new bounds for non-abelian number fields.
LA - eng
KW - $L$-functions; Dedekind zeta functions; number fields; class number; Class numbers; cubic and quartic extensions; cyclotomic fields; zeta functions
UR - http://eudml.org/doc/249456
ER -

References

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