Non-vanishing of class group L-functions at the central point
Annales de l'Institut Fourier, Volume 54 (2004) no. 4, pp. 831-847.

Let K=(-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 pD (1-p -1 ) of the h distinct L-functions L K (s,χ) do not vanish at the central point s=1/2.

Étant donné un corps quadratique imaginaire K=(-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 pD (1-p -1 ) des h fonctions L distinctes L K (s,χ) ne s’annulent pas au point central s=1/2.

DOI: 10.5802/aif.2035
Classification: 11R42, 11M41, 11F67
Keywords: non-vanishing results, $L$-functions, imaginary quadratic fields, mollifier
Mot clés : théorèmes de non-annulation, fonctions $L$, corps quadratique imaginaire, fonction de mollification
Blomer, Valentin 1

1 University of Toronto, Department of Mathematics, 100 St. George Street, Toronto M5S 3G3, Ontario, (Canada)
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Blomer, Valentin. Non-vanishing of class group $L$-functions at the central point. Annales de l'Institut Fourier, Volume 54 (2004) no. 4, pp. 831-847. doi : 10.5802/aif.2035. http://archive.numdam.org/articles/10.5802/aif.2035/

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