CM cycles and nonvanishing of class group L--functions
- Autores: Riad Masri
- Localización: Mathematical research letters, ISSN 1073-2780, Vol. 17, Nº 4, 2010, págs. 749-760
- Idioma: inglés
- DOI: 10.4310/mrl.2010.v17.n4.a13
- Enlaces
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Resumen
Let $K$ be a totally imaginary quadratic extension of a totally real number field $F$, and assume that $F$ has narrow ideal class number 1. Let $\chi$ be a character of the ideal class group $\Cl(K)$ of $K$, and let $L_K(\chi,s)$ be its associated $L$--function. In this paper we prove that for all $\epsilon > 0$, \begin{align*} \# \{\chi \in \textrm{CL}(K)^{\wedge}:~L_K(\chi,\frac{1}{2}) \neq 0\} \gg_{\epsilon, F} d_K^{\frac{1}{100}-\epsilon} \end{align*} as the absolute discriminant $d_K \rightarrow \infty$.
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