Skip to main content
6 events
when toggle format what by license comment
Jun 30, 2014 at 5:31 history edited 7-adic CC BY-SA 3.0
added 29 characters in body
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
added 168 characters in body
Jun 30, 2014 at 4:35 history asked 7-adic CC BY-SA 3.0