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| The Generalized Prime Number Theorem for Automorphic L-Functions |
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Citation： |
Hengcai TANG.The Generalized Prime Number Theorem for Automorphic L-Functions[J].Chinese Annals of Mathematics B,2009,30(3):251~260 |
| Page view： 1744
Net amount： 1310 |
Authors： |
Hengcai TANG; |
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| Abstract： |
Let $\pi$ and $\pi'$ be automorphic irreducible cuspidal
representations of ${\rm GL}_m(\BQ_\BA)$ and ${\rm
GL}_{m'}(\BQ_\BA)$, respectively, and $L(s,\pi\times\wt\pi')$ be the
Rankin-Selberg $L$-function attached to $\pi$ and $\pi'$. Without
assuming the Generalized Ramanujan Conjecture (GRC), the author
gives the generalized prime number theorem for
$L(s,\pi\times\wt\pi')$ when $\pi\cong\pi'$. The result generalizes
the corresponding result of Liu and Ye in 2007. |
Keywords： |
Perron’s formula, Prime number theorem, Rankin-Selberg L-functions |
Classification： |
11F70, 11M26, 11M41 |
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