A purely analytical lower bound for L(1,χ)
Annales mathématiques Blaise Pascal, Volume 16 (2009) no. 2, pp. 259-265.

We give a simple proof of L(1,χ)q2 ω(q) when χ is an odd primitiv quadratic Dirichlet character of conductor q. In particular we do not use the Dirichlet class-number formula.

Nous donnons une preuve simple de l’inégalité L(1,χ)q2 ω(q) lorsque χ est un caractère quadratique primitif impair. En particulier, nous n’utilisons pas la formule de Dirichlet liant L(1,χ) et e nombre de classes.

DOI: 10.5802/ambp.265
Classification: 11N05
Keywords: Lower bound for $L(1,\chi )$, Dirichlet class number formula
Olivier Ramaré 1

1 Laboratoire CNRS Paul Painlevé Université Lille I 59 655 Villeneuve d’Ascq Cedex
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Olivier Ramaré. A purely analytical lower bound for $L(1,\chi )$. Annales mathématiques Blaise Pascal, Volume 16 (2009) no. 2, pp. 259-265. doi : 10.5802/ambp.265. https://ambp.centre-mersenne.org/articles/10.5802/ambp.265/

[1] Dorian Goldfeld Gauss’s class number problem for imaginary quadratic fields, Bull. Amer. Math. Soc. (N.S.), Volume 13 (1985) no. 1, pp. 23-37 | DOI | MR | Zbl

[2] Joseph Oesterlé Nombres de classes des corps quadratiques imaginaires, Astérisque (1985) no. 121-122, pp. 309-323 (Seminar Bourbaki, Vol. 1983/84) | Numdam | MR | Zbl

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