Timeline for S-transformation of generalized Eisenstein series

6 events

when toggle format	what		by	license	comment
Dec 12, 2011 at 7:25	vote	accept	phoboid
Dec 11, 2011 at 17:42	answer	added	paul garrett		timeline score: 2
Dec 11, 2011 at 8:29	comment	added	phoboid		@paul garrett: Sorry for being unclear, the $\sigma$'s are defined as $\sigma^{\psi,\phi}(n) = \sum_{m\mid n, m>0} \psi(n/m) \phi(m) m$, so it is basically a sum-of-divisors function weighted by the Dirichlet characters.
Dec 10, 2011 at 23:09	comment	added	paul garrett		@phoboid: Perhaps the $\sigma^{\psi,\phi}$ notation is not universal... can it be explained briefly? This might enable further answers.
Dec 10, 2011 at 20:45	comment	added	B R		Personally, I think it is difficult to understand how the Eisenstein series transforms using the $q$-expansion. If I were you (in the notation of D-S, Section 4.6), I'd be stuck with noting that $E_2^{\psi,\phi}$ is a multiple of $G_2^{\psi,\phi}$, which is a weighted sum of $G_2^{\bar v}$, which is the sum of two functions, $f^{\bar v}_2(\tau)$ and $G_2(\tau)/N$. Maybe someone else knows a smarter way.
Dec 10, 2011 at 18:58	history	asked	phoboid	CC BY-SA 3.0