On the error function in the asymptotic formula for the counting function of k-full numbers

On a question of A. Schinzel: Omega estimates for a special type of arithmetic functions

“…The conclusion from this result to Theorem 1 is easy and has many analogues in the literature; see [1,9,10]. Nevertheless, we supply the details for convenience of the reader.…”

“…For any arithmetic function H ∈ C with a generating function F H ( ) according to (1), it holds true that, as → ∞,…”

On an asymptotic formula of Srinivasa Ramanujan

“…Note that our X = (log T ) 8/δ . The horizontal portions contribute an error which is (log T )X δ/4 e −(log T ) 3 1 because of the presence of the Γ (w) in the integrand, whereas the vertical line integral on u = −δ/8 contributes an error which is (log T )X −δ/8 1 with our choice of X. Note that…”

“…We note here that an analogue of Theorem A for the "sums of two squares" function r(n) was dealt with by M. Kühleitner (see [7]). We also refer to the related papers [2], [3], [12] and [20].…”

On the error term of an asymptotic formula of Ramanujan

“…For some more general interesting results, we refer to for example [1], [2], [3] and [23]; we also mention some related references [4], [14] and [27].…”