Fractional part sums and lattice points

Proceedings of the Edinburgh Mathematical Society

Volumn 41, Issue 3, 1998, Pages 497-515

  Nowak, Werner Georg ^a  

^a UNIVERSITY OF NATURAL RESOURCES AND LIFE SCIENCES   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22444452230     PISSN: 00130915     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0013091500019854     Document Type: Article

References (26)

1. E. BOMBIER: and H. IWANIEC, On the order of f + i'r), Ann. Scuola Norm. Sup. Pisa Ser. IV, 13 (1986), 449-472.
2. M. BRANTON and P. SARGOS, Points entiers au voisinage d'une courbe plane àtrès faible courbure, Bull. Sei. Math. 118 (1994), 15-28.
3. K. CHANDRASEKHARAN and R. NARASIMHAN, On the mean value of the error term for a class of arithmetic functions, Ada Math. 112 (1964), 41-67.
4. J. G. VAN DER CORPUT, Zahlentheoretische Abschätzungen mit Anwendung auf Gitterpunktprobleme, Math. Z. 17 (1923), 250-259.
5. J. G. VAN DER CORPUT, Neue zahlentheoretische Abschätzungen, Math. Ann. 89 (1923), 215-254.
6. S. W. GRAHAM and G. KOLESNIK, Van der Corput's method of exponential sums (Cambridge University Press, Cambridge, 1991).
7. J. L. HAFNER, New omega theorems for two classical lattice point problems, Invent. Math. 63 (1981), 181-186.
8. J. L. HAFNER, On the average order of a class of arithmetical functions, J. Number Theory 15 (1982), 36-76.
9. E. HLAWKA, Über die Zetafunktion konvexer Körper, Monatsh Math. 54 (1950), 100-107.
10. M. N. HUXLEY, Exponential sums and rounding error, J. London Math. Soc. (2) 43 (1991), 367-384.
11. M. N. HUXLEY, Exponential sums and lattice points II, Proc. London Math. Soc. 66 (1993), 279-301.
12. M. N. HUXLEY, The mean lattice point discrepancy, Proc. Edinburgh Math. Soc. 38 (1995), 523-531.
13. M. N. HUXLEY, Area, lattice points, and exponential sums (LMS Monographs, New Ser. 13, Oxford 1996).
14. M. N. HUXLEY and P. SARGOS, Points entiers au voisinage d'une courbe plane de classe C", Acta Arithm. 69 (1995), 359-366.
15. H. IWANIEC and C. J. MOZZOCHI, On the divisor and circle problems, J. Number Theory 29 (1988), 60-93.
16. I. KâTAI, The number of lattice points in a circle, Ann. Univ. Sei. Budap. Rolando Eotvos. Sect. Math. 8 (1965), 39-60.
17. E. KRäTZEL, Lattice Points (Dt. Verl. d. Wiss., Berlin, 1988).
18. L. KUIPERS and H. NIEDERREITER, Uniform distribution of sequences (J. Wiley & Sons, New York 1974).
19. W. MüLLER, On the average order of the lattice rest of a convex body, Acta Arithm. 80 (1997), 89-100.
20. W. G. NOWAK, Einige Beiträge zur Theorie der Gitterpunkte, in Zahlentheoretische Analysis (Seminar 1980-1982, ed. E. Hlawka, Springer LNM 1114, 1985), pp. 98-117.
21. W. G. NOWAK, An fi-estimate for the lattice rest of a convex planar domain, Proc. Roy. Soc. Edinburgh Sect. A 100 (1985), 295-299.
22. W. G. NOWAK, On the average order of the lattice rest of a convex planar domain, Proc. Cambridge Philos. Soc. 98 (1985), 1-4.
23. D. REDMOND, Mean value theorems for a class of Dirichlet series, Pacific J. Math. 78 (1978), 191-231.
24. H. P. F. SWINNERTON-DYER, The number of lattice points on a convex curve, J. Number Theory 6 (1974), 128-135.
25. J. D. VAALER, Some extremal problems in Fourier analysis, Bull. Amer. Math. Soc. (2) 12(1985), 183-216.
26. I. M. VINOGRADOV, Selected works (eds. L. D. Faddeev et al., Springer, BerlinHeidelberg 1985).