Timeline for Constant coefficient of Eisenstein series
Current License: CC BY-SA 4.0
2 events
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| Sep 29, 2021 at 20:17 | comment | added | Peter Humphries | You misread Corollary 2.5: they first multiply the Eisenstein series by $\zeta(2s + 1)$ to get a "completed" Eisenstein series $E^{\ast}$, then conclude that $E^{\ast}$ (not $E$!) is holomorphic except possibly at $s = 1/2$. The key point is that the completed zeta function $\pi^{-s/2} \Gamma(s/2) \zeta(s)$ has poles only at $s = 0$ and $s = 1$, and otherwise is holomorphic; in particular, every term in the Fourier-Whittaker expansion in Theorem 2.4 is holomorphic. | |
| Sep 29, 2021 at 17:40 | history | asked | Aersk | CC BY-SA 4.0 |