Geodesic
Non-vanishing of class group L-functions at the central point
[Non-annulation des fonctions L de groupes de classes au point central]
Blomer, Valentin1 idref
1University of Toronto, Department of Mathematics, 100 St. George Street, Toronto M5S 3G3, Ontario, (Canada)
Annales de l'Institut Fourier, Tome 54 (2004) no. 4, pp. 831-847
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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.

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.

DOI : 10.5802/aif.2035
Classification : 11R42, 11M41, 11F67
Keywords: non-vanishing results, $L$-functions, imaginary quadratic fields, mollifier
Mots-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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     title = {Non-vanishing of class group $L$-functions at the central point},
     journal = {Annales de l'Institut Fourier},
     pages = {831--847},
     year = {2004},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
     number = {4},
     doi = {10.5802/aif.2035},
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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

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