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Myshkin
Myshkin
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Let $F$ be a number field. Let and let $\pi$ be a cuspidal automorphic representation of $GL_n(\mathbb{A_F})$. Do

Do we know that $L(s,\pi\times \tilde\pi)$ has a simple pole at $s=1$? Do

Do we know that $\frac{L(s,\pi\times \tilde\pi)}{\zeta_F(s)}$ is holomorphic at $s=1$?

Let $F$ be a number field. Let $\pi$ be a cuspidal automorphic representation of $GL_n(\mathbb{A_F})$. Do we know that $L(s,\pi\times \tilde\pi)$ has a simple pole at $s=1$? Do we know that $\frac{L(s,\pi\times \tilde\pi)}{\zeta_F(s)}$ is holomorphic at $s=1$?

Let $F$ be a number field and let $\pi$ be a cuspidal automorphic representation of $GL_n(\mathbb{A_F})$.

Do we know that $L(s,\pi\times \tilde\pi)$ has a simple pole at $s=1$?

Do we know that $\frac{L(s,\pi\times \tilde\pi)}{\zeta_F(s)}$ is holomorphic at $s=1$?

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7-adic
7-adic
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Poles of Rankin-Selberg $L(s,\pi\times\tilde \pi)$?

Let $F$ be a number field. Let $\pi$ be a cuspidal automorphic representation of $GL_n(\mathbb{A_F})$. Do we know that $L(s,\pi\times \tilde\pi)$ has a simple pole at $s=1$? Do we know that $\frac{L(s,\pi\times \tilde\pi)}{\zeta_F(s)}$ is holomorphic at $s=1$?