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 
1 University 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

Voir la notice de l'article provenant de la source Numdam

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) 
@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{\textquoteright}institut Fourier},
     volume = {54},
     number = {4},
     year = {2004},
     doi = {10.5802/aif.2035},
     mrnumber = {2111013},
     zbl = {1063.11040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/aif.2035/}
}
TY  - JOUR
AU  - Blomer, Valentin
TI  - Non-vanishing of class group $L$-functions at the central point
JO  - Annales de l'Institut Fourier
PY  - 2004
SP  - 831
EP  - 847
VL  - 54
IS  - 4
PB  - Association des Annales de l’institut Fourier
UR  - http://geodesic.mathdoc.fr/articles/10.5802/aif.2035/
DO  - 10.5802/aif.2035
LA  - en
ID  - AIF_2004__54_4_831_0
ER  - 
%0 Journal Article
%A Blomer, Valentin
%T Non-vanishing of class group $L$-functions at the central point
%J Annales de l'Institut Fourier
%D 2004
%P 831-847
%V 54
%N 4
%I Association des Annales de l’institut Fourier
%U http://geodesic.mathdoc.fr/articles/10.5802/aif.2035/
%R 10.5802/aif.2035
%G en
%F 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

Cité par Sources :