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- W4287989466 abstract "Let $F(s)=sum_{n=1}^{infty}frac{a_n}{n^s}$ be a Dirichlet series in the axiomatically defined class ${mathfrak A}^{#}$ . The class ${mathfrak A}^{#}$ is known to contain the extended Selberg class ${mathcal S}^{#}$, as well as all the $L$-functions of automorphic forms on $GL_n/K$, where $K$ is a number field. Let $d$ be the degree of $F(s)$. We show that $sum_{n<X}|a_n|=Omega(X^{frac{1}{2}+frac{1}{2d}})$, and hence, that the abscissa of absolute convergence of $sigma_a$ of $F(s)$ must satisfy $sigma_age 1/2+1/2d$." @default.
- W4287989466 created "2022-07-26" @default.
- W4287989466 creator A5008914304 @default.
- W4287989466 date "2021-05-14" @default.
- W4287989466 modified "2023-09-29" @default.
- W4287989466 title "On the absolute convergence of automorphic Dirichlet series" @default.
- W4287989466 doi "https://doi.org/10.48550/arxiv.2105.06957" @default.
- W4287989466 hasPublicationYear "2021" @default.
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