The asymptotic behaviour of the mean-square of fractional part sums

Authors
Kuhleitner, M Nowak, WG
Citation
M. Kuhleitner et Wg. Nowak, The asymptotic behaviour of the mean-square of fractional part sums, P EDIN MATH, 43, 2000, pp. 309-323
Citations number
20
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
ISSN journal
00130915 → ACNP
Volume
43
Year of publication
2000
Part
2
Pages
309 - 323
Database
ISI
SICI code
0013-0915(200006)43:<309:TABOTM>2.0.ZU;2-1
Abstract
In this article we consider sums S(t) = Sigma(n)psi(tf(n/t)), where psi den otes, essentially, the fractional part minus 1/2, f is a C-4-function with f " non-vanishing, and summation is extended over an interval of order t. F or the mean-square of S(t), an asymptotic formula is established. If f is a lgebraic this can be sharpened by the indication of an error term.