caa a22 4500 388024178 CHVBK 20180307124932.0 cr unu---uuuuu 161130e199810 xx s 000 0 eng 10.1017/S0013091500019854 doi S0013091500019854 pii (NATIONALLICENCE)cambridge-10.1017/S0013091500019854 Nowak Werner Georg Institut für Mathematik, Universität für Bodenkultur, A-1180 Wien, Austria, E-mail: nowak@mail.boku.ac.at Fractional part sums and lattice points [Elektronische Daten] [Werner Georg Nowak] The objective of this article are sums S(M)=∑n;ψ(Mf(n/M)) where ψdenotes essentially the fractional part minus ½, f is a C4-function with fn nonvanishing, and summation is extended over an interval of order M. For S(M) an Ω-estimate and a mean-square bound is obtained. Applications to problems concerning the number of lattice points in large planar domains are discussed. Copyright © Edinburgh Mathematical Society 1998 Proceedings of the Edinburgh Mathematical Society Cambridge University Press 41/3(1998-10), 497-515 0013-0915 41:3<497 1998 41 PEM https://doi.org/10.1017/S0013091500019854 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0013091500019854 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Nowak Werner Georg Institut für Mathematik, Universität für Bodenkultur, A-1180 Wien, Austria, E-mail: nowak@mail.boku.ac.at NATIONALLICENCE 773 0- Proceedings of the Edinburgh Mathematical Society Cambridge University Press 41/3(1998-10), 497-515 0013-0915 41:3<497 1998 41 PEM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge