no. 4
Non-vanishing of class group L-functions at the central point  [ Non-annulation des fonctions L de groupes de classes au point central ]
Annales de l'Institut Fourier, Tome 54 (2004) no. 4, pp. 831-847.

Étant donné un corps quadratique imaginaire K=ℚ(-D), notons h son nombre de classes. Nous montrons qu’il existe une constante c telle que pour D assez grand, au moins c·h∏ p∣D (1-p -1 ) des h fonctions L distinctes L K (s,χ) ne s’annulent pas au point central s=1/2.

Let K=ℚ(-D) be an imaginary quadratic field, and denote by h its class number. It is shown that there is an absolute constant c>0 such that for sufficiently large D at least c·h∏ p∣D (1-p -1 ) of the h distinct L-functions L K (s,χ) do not vanish at the central point s=1/2.

DOI : https://doi.org/10.5802/aif.2035
Classification : 11R42,  11M41,  11F67
Mots clés : théorèmes de non-annulation, fonctions L, corps quadratique imaginaire, fonction de mollification 
@article{AIF_2004__54_4_831_0,
     author = {Blomer, Valentin},
     title = {Non-vanishing of class group $L$-functions at the central point},
     journal = {Annales de l'Institut Fourier},
     pages = {831--847},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {4},
     year = {2004},
     doi = {10.5802/aif.2035},
     zbl = {1063.11040},
     mrnumber = {2111013},
     language = {en},
     url = {www.numdam.org/item/AIF_2004__54_4_831_0/}
}
Blomer, Valentin. Non-vanishing of class group $L$-functions at the central point. Annales de l'Institut Fourier, Tome 54 (2004) no. 4, pp. 831-847. doi : 10.5802/aif.2035. http://www.numdam.org/item/AIF_2004__54_4_831_0/

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