论文标题
非关键$ l $ $ $价值的HIDA家庭
Non-vanishing of critical $L$-values in Hida families
论文作者
论文摘要
我们将$ l（F，χ，J）$的消失作为$ f $在$ p $ -ADIC HIDA家族中的所有古典形式运行（包括$ p $ $ p $的任意nebentype的表格），$χ$通过$ p $ popper指挥的所有字符运行，$ j $是关键值。我们表明，如果这些$ l $价值中的许多无限消失（除了被强迫因其功能方程式而消失的$ LAVE），那么这种消失的无限必须非常规律，因此实际上通常可以在任何给定的示例中排除这种可能性。确实，我们系统地验证了这种常规的消失在多个HIDA家族中不会发生通过多种二次字符扭曲，通过计算通过过度缩合的模块化符号来计算相应的两变量$ p $ p $ -p $ ad-adic $ l $ functions。
We study the vanishing of $L(f,χ,j)$ as $f$ runs through all classical forms in a $p$-adic Hida family (including forms with arbitrarily high nebentype at $p$), $χ$ runs through all characters of $p$-power conductor, and $j$ is a critical value. We show that if infinitely many of these $L$-values vanish (apart from the ones forced to vanish by the sign of their functional equation) then this infinitude of vanishing must be exceptionally regular, so regular in fact that one can typically rule out this possibility in any given example. Indeed, we systematically verified that such regular vanishing does not occur in multiple Hida families twisted by a wide range of quadratic characters by computing the corresponding two-variable $p$-adic $L$-functions via overconvergent modular symbols.
