Comptes Rendus
no. 8
Majorations explicites de |L(1,χ)| (quatrième partie)
Stéphane R. Louboutin1
1 Institut de mathématiques de Luminy, UPR 9016, 163 avenue de Luminy, case 907, 13288 Marseille cedex 9, France
Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 625-628.

Nous montrons que pour tout caractère de Dirichlet χ pair, primitif et de conducteur qχ>1 impair, nous avons (1-χ(2)2)L(1,χ)⩽14(logqχ+κ) avec κ :=2+γ−log(π/4)=2.81878….

We prove that for any even primitive Dirichlet character χ of odd conductor qχ>1 we have (1-χ(2)2)L(1,χ)⩽14(logqχ+κ), where κ:=2+γ−log(π/4)=2.81878….

Reçu le :
Révisé le :
Publié le :
DOI : 10.1016/S1631-073X(02)02333-6

Stéphane R. Louboutin 1

1 Institut de mathématiques de Luminy, UPR 9016, 163 avenue de Luminy, case 907, 13288 Marseille cedex 9, France 
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Stéphane R. Louboutin. Majorations explicites de |L(1,χ)| (quatrième partie). Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 625-628. doi : 10.1016/S1631-073X(02)02333-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02333-6/

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  • Stéphane R. Louboutin Upper bounds on L(1,χ) taking into account a finite set of prime ideals, Acta Arithmetica, Volume 182 (2018) no. 3, pp. 249-269 | DOI:10.4064/aa170426-23-10 | Zbl:1422.11230
  • Shinya Okumura; Shingo Sugiyama; Masaya Yasuda; Tsuyoshi Takagi Security analysis of cryptosystems using short generators over ideal lattices, Japan Journal of Industrial and Applied Mathematics, Volume 35 (2018) no. 2, pp. 739-771 | DOI:10.1007/s13160-018-0306-z | Zbl:1404.94103
  • Shingo Sugiyama On Analysis of Recovering Short Generator Problems via Upper and Lower Bounds of Dirichlet L-Functions: Part 1, Mathematical Modelling for Next-Generation Cryptography, Volume 29 (2018), p. 257 | DOI:10.1007/978-981-10-5065-7_14
  • Shinya Okumura On Analysis of Recovering Short Generator Problems via Upper and Lower Bounds of Dirichlet L-functions: Part 2, Mathematical Modelling for Next-Generation Cryptography, Volume 29 (2018), p. 279 | DOI:10.1007/978-981-10-5065-7_15
  • Stéphane R. Louboutin Upper bounds on L(1,χ) taking into account ramified prime ideals, Journal of Number Theory, Volume 177 (2017), pp. 60-72 | DOI:10.1016/j.jnt.2017.01.010 | Zbl:1428.11200
  • Władysław Narkiewicz The First Years, Rational Number Theory in the 20th Century (2012), p. 13 | DOI:10.1007/978-0-85729-532-3_2
  • Stéphane R. Louboutin Upper bounds for residues of Dedekind zeta functions and class numbers of cubic and quartic number fields, Mathematics of Computation, Volume 80 (2011) no. 275, pp. 1813-1822 | DOI:10.1090/s0025-5718-2011-02457-9 | Zbl:1282.11150
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  • Stéphane R. Louboutin Explicit upper bounds for values at s=1 of Dirichlet L-series associated with primitive even characters., Journal of Number Theory, Volume 104 (2004) no. 1, pp. 118-131 | DOI:10.1016/s0022-314x(03)00159-8 | Zbl:1044.11082
  • Stéphane Louboutin Explicit lower bounds for residues at s=1 of Dedekind zeta functions and relative class numbers of CM-fields, Transactions of the American Mathematical Society, Volume 355 (2003) no. 8, pp. 3079-3098 | DOI:10.1090/s0002-9947-03-03313-0 | Zbl:1026.11085
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Cité par 12 documents. Sources : Crossref, zbMATH

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