论文标题
在大的Iwasawa上
On large Iwasawa $λ$-invariants of imaginary quadratic function fields
论文作者
论文摘要
令$ \ ell $为质量数字，$ q $为$ \ ell $的功率。给定一个奇数的素数$ p $和一个假想的二次扩展$ f $ f $ of RICANTION函数字段$ \ MATHBB {F} _Q（T）$，让$λ_p（f）$表示iwasawa $λ$ -Invariant的常数$ \ Mathbb {Z} z} _p $ f $ $ f $ f $ f $ f $。我们表明，对于任何数字$ r> 0 $，所有足够大的值的$ q \ not \ equiv 1 \ mod {p} $，与$λ_p（f）\ geq r $的属性相关的想象二次二次字段$ f/f/f/f/f/f/f/f/f/f/f/f/f/f/f/f/f/f/f/f/f/f/f/主要结果是由于艾伦伯格·韦卡茨·韦斯特兰（Ellenberg-Venkatesh-Westerland）最近无条件定理对假想二次功能领域的分布而言。
Let $\ell$ be a prime number and $q$ be a power of $\ell$. Given an odd prime number $p$ and an imaginary quadratic extension $F$ of the rational function field $\mathbb{F}_q(T)$, let $λ_p(F)$ denote the Iwasawa $λ$-invariant of the constant $\mathbb{Z}_p$-extension of $F$. We show that for any number $r>0$ and all large enough values of $q\not\equiv 1\mod{p}$, there is a positive proportion of imaginary quadratic fields $F/\mathbb{F}_q(T)$ with the property that $λ_p(F)\geq r$. The main result is proved as a consequence of recent unconditional theorems of Ellenberg-Venkatesh-Westerland on the distribution of class groups of imaginary quadratic function fields.
