Timeline for Symmetric Fifth Power Lift of GL(2) Automorphic Form
Current License: CC BY-SA 3.0
6 events
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Jun 30, 2014 at 5:31 | history | edited | 7-adic | CC BY-SA 3.0 |
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Jun 30, 2014 at 5:26 | comment | added | Lucia | You might want to clarify the exact question then. Presently you only ask for holomorphy on "any small area to the left of $1$". | |
Jun 30, 2014 at 5:25 | comment | added | 7-adic | I do need a larger region. And moreover the standard zero free region of $Sym^3$ does not say anything about the real line. | |
Jun 30, 2014 at 5:23 | comment | added | Lucia | You could take Rankin-Selberg of $\text{Sym}^2$ and $\text{Sym}^3$, which would factor as $\text{Sym}^5$ times $\text{Sym}^3$ times $\pi$. Since the Rankin-Selberg is holomorphic, one should get holomorphy of $\text{Sym}^5$ in any zero free region for $\pi$ and $\text{Sym}^3$. The usual arguments would give a small zero-free region to the left of $1$ for these two $L$-functions, and hence a small region of holomorphy for $\text{Sym}^5$. Is this what you were looking for, or did you need a larger region? | |
Jun 30, 2014 at 5:15 | history | edited | 7-adic | CC BY-SA 3.0 |
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Jun 30, 2014 at 4:35 | history | asked | 7-adic | CC BY-SA 3.0 |