论文标题
无限的许多添加性扭曲$ l $ functions的零零在关键线上
Infinitely many zeros of additively twisted $L$-functions on the critical line
论文作者
论文摘要
对于$ f $ cuspidal模块化形式，用于组的$γ_0（n）$的整体重量或半集成重量，$ n $ a $ a倍的$ 4 $如果重量是半集成的，我们研究$ l $ function $ f $ f $ f $ twise twist audmitive twist twistive twist的零，并由附加符号$ e^n \ e^n \ frac} $ $ \ frac {p} {q} \ in \ mathbb {q} $。我们证明，对于某些$ f $和$ \ frac {p} {q} \ in \ mathbb {q} $，添加性扭曲的$ l $ - 功能在关键行上具有无限的许多零。我们开发了Hardy-Littlewood方法的变体，该方法使用分布来证明结果。
For $f$ a cuspidal modular form for the group $Γ_0(N)$ of integral or half-integral weight, $N$ a multiple of $4$ in case the weight is half-integral, we study the zeros of the $L$-function attached to $f$ twisted by an additive character $e^{2πi n \frac{p}{q}}$ with $\frac{p}{q}\in \mathbb{Q}$. We prove that for certain $f$ and $\frac{p}{q}\in \mathbb{Q}$, the additively twisted $L$-function has infinitely many zeros on the critical line. We develop a variant of the Hardy-Littlewood method which uses distributions to prove the result.
