Étant donné un corps quadratique imaginaire , notons son nombre de classes. Nous montrons qu’il existe une constante telle que pour assez grand, au moins des fonctions distinctes ne s’annulent pas au point central .
Let be an imaginary quadratic field, and denote by its class number. It is shown that there is an absolute constant such that for sufficiently large at least of the distinct -functions do not vanish at the central point .
Classification : 11R42, 11M41, 11F67
Mots clés : théorèmes de non-annulation, fonctions , 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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