no. 1
Ordre de grandeur de L(1,χ) et de L ' (1,χ)
Annales de l'Institut Fourier, Tome 29 (1979) no. 1, pp. 125-135.

On étudie sommairement la distribution des valeurs de L ′ (1,χ) (χ : caractère de Dirichlet primitif réel) et on constate qu’on a en général L ′ (1,χ)<π 2 /6; on démontre par ailleurs que si L ′ (1,χ)<(π 2 /6)-ε, alors L(1,χ)>c(ε)/logk (k : conducteur de χ; c(ε): constante positive effectivement calculable.

The paper gives a rough description of the distribution of values of L ′ (1,χ) (χ, a real primitive residue character), which usually lie under π 2 /6; and a proof of the following theorem: if L ′ (1,χ)<(π 2 /6)-ε, then L(1,χ)>c(ε)/logk (k the conductor of χ; c(ε), a positive, computable constant.

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     author = {Joly, Jean-Ren\'e and Moser, Claude},
     title = {Ordre de grandeur de $L(1,\chi )$ et de $L^{\prime }(1,\chi )$},
     journal = {Annales de l'Institut Fourier},
     pages = {125--135},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {29},
     number = {1},
     year = {1979},
     doi = {10.5802/aif.730},
     mrnumber = {80d:10060},
     zbl = {0386.10026},
     language = {fr},
     url = {http://archive.numdam.org/articles/10.5802/aif.730/}
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Joly, Jean-René; Moser, Claude. Ordre de grandeur de $L(1,\chi )$ et de $L^{\prime }(1,\chi )$. Annales de l'Institut Fourier, Tome 29 (1979) no. 1, pp. 125-135. doi : 10.5802/aif.730. http://archive.numdam.org/articles/10.5802/aif.730/

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