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Cancellation of two classes of dirichlet coefficients over Beatty sequences
Canadian Mathematical Bulletin ( IF 0.5 ) Pub Date : 2021-04-20 , DOI: 10.4153/s0008439521000242
Qiang Ma 1
Affiliation  

Let $\pi $ be an automorphic irreducible cuspidal representation of $\mathrm{GL}_{m}$ over $\mathbb {Q}$ . Denoted by $\lambda _{\pi }(n)$ the nth coefficient in the Dirichlet series expansion of $L(s,\pi )$ associated with $\pi $ . Let $\pi _{1}$ be an automorphic irreducible cuspidal representation of $\mathrm{SL}(2,\mathbb {Z})$ . Denoted by $\lambda _{\pi _{1}\times \pi _{1}}(n)$ the nth coefficient in the Dirichlet series expansion of $L(s,\pi _{1}\times \pi _{1})$ associated with $\pi _{1}\times \pi _{1}$ . In this paper, we study the cancellations of $\lambda _{\pi }(n)$ and $\lambda _{\pi _{1}\times \pi _{1}}(n)$ over Beatty sequences.



中文翻译:

Beatty序列上两类狄利克雷系数的对消

$\pi $ $\mathrm{GL}_{m}$ $\mathbb {Q}$ 上的一个自守不可约尖表示。用 $\lambda _{\pi }(n)$ 表示与 $\pi $相关的 $L(s,\pi )$ 的狄利克雷级数展开中的第n个系数。令 $\pi _{1}$ $\mathrm{SL}(2,\mathbb {Z})$ 的自守不可约尖瓣表示。记为 $L(s,\pi _{1}\times \的狄利克雷级数展开中的第n个系数 $\lambda _{\pi _{1 }\times pi _{1})$ $\pi _{1}\times \pi _{1}$ 。在本文中,我们研究了 Beatty 序列上 $\lambda _{\pi }(n)$ $\lambda _{\pi _{1}\times \pi _{1}}(n)$ 的抵消。

更新日期:2021-04-20
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