Timeline for Estimates for $\sum_{n\leq x} d(n)^a$

9 events

when toggle format	what		by	license	comment
Nov 18, 2017 at 1:04	comment	added	GH from MO		@reuns: I think for $a>0$ not an integer (and more generally for $a\in\mathbb{C}$ not an integer), the best tool is the Selberg-Delange method, see Tenenbaum's book for that. (And disregard my previous comment if you saw it, I deleted it quickly.)
Nov 17, 2017 at 21:31	comment	added	reuns		How do you deal with Mellin inversion for non-meromorphic Dirichlet series, do you expand in real powers of $s-1$, then what ?
S Nov 17, 2017 at 16:10	history	suggested	Dimitris Koukoulopoulos	CC BY-SA 3.0	Added reference for a more precise asymptotic formula
Nov 17, 2017 at 15:23	review	Suggested edits
S Nov 17, 2017 at 16:10
Nov 17, 2017 at 13:31	history	edited	js21	CC BY-SA 3.0	deleted 1 character in body
Nov 17, 2017 at 10:38	vote	accept	kodlu
Nov 17, 2017 at 9:51	comment	added	Will Sawin		In the special case $a=2$, the Euler product is $\prod_p ( 1 - 1/p^2) = \zeta(2)^{-1}= 6/\pi^2$ and the gamma factor is $\Gamma(4) = 6$, so the constant is $1/\pi^2$. Moreover one can probably use the formula $F(s) = \zeta(2s)^{-1}$ to get a better error term.
Nov 17, 2017 at 9:14	history	edited	js21	CC BY-SA 3.0	added 135 characters in body
Nov 17, 2017 at 9:04	history	answered	js21	CC BY-SA 3.0