Primitive lattice points in planar domains

Acta Arithmetica

Volumn 142, Issue 3, 2010, Pages 267-302

  Baker, Roger C ^a  

^a BRIGHAM YOUNG UNIVERSITY   (United States)

Author keywords

Compact convex set; Exponential sums; Hlawka zeta function; Primitive lattice points

Indexed keywords

EID: 77953772195     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa142-3-4     Document Type: Article

References (21)

1. T. M. Apostol, Mathematical Analysis, Addison-Wesley, 1957.
2. R. C. Baker, Sums of two relatively prime cubes, Acta Arith. 129 (2007), 103-146.
3. -, Sums of two relatively prime k-th powers, Funct. Approx., to appear.
4. J. G. van der Corput, Über Gitterpunkte in der Ebene, Math. Ann. 81 (1920), 1-20.
5. S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, Cambridge Univ. Press, 1991.
6. G. Harman, Prime-Detecting Sieves, Princeton Univ. Press, 2007.
7. D. Hensley, The number of lattice points within a contour and visible from the origin, Pacific J. Math. 166 (1994), 295-304.
8. M. N. Huxley, The mean lattice point discrepancy, Proc. Edinburgh Math. Soc. 38 (1995), 525-531.
9. -, Exponential sums and lattice points. III, Proc. London Math. Soc. 87 (2003), 591-609.
10. M. N. Huxley and W. G. Nowak, Primitive lattice points in convex planar domains, Acta Arith. 76 (1996), 271-283.
11. M. Kühleitner and W. G. Nowak, The asymptotic behaviour of the mean-square of fractional part sums, Proc. Edinburgh Math. Soc. 43 (2000), 309-323.
12. H. L. Montgomery and R. C. Vaughan, The distribution of squarefree numbers, in: Recent Progress in Analytic Number Theory, Vol. 1, Academic Press, 1981, 247-256.
13. B. Z. Moroz, On the number of primitive lattice points in plane domains, Monatsh. Math. 99 (1985), 37-43.
14. W. Müller, Lattice points in convex planar domains: power moments with an application to primitive lattice points, in: Proc. Conf. on Analytic and Elementary Number Theory (Vienna, 1996), Inst. Math. und Statist. Univ. Wien, 1996, 189-199.
15. W. G. Nowak, Fractional part, sums and lattice points, Proc. Edinburgh Math. Soc. 41 (1998), 497-515.
16. O. Robert and P. Sargos, Three-dimensional exponential sums with monomials, J. Reine Angew. Math. 591 (2006), 1-20.
17. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., Oxford Univ. Press, 1986.
18. J. D. Vaaler, Some extremal problems in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985), 183-216.
19. N. Watt, Exponential sums and the Riemann zeta-function II, J. London Math. Soc. 39 (1989), 385-404.
20. J. Wu, On the primitive circle problem, Monatsh. Math. 135 (2002), 69-81.
21. W. G. Zhai, On primitive lattice points in planar domains, Acta Arith. 109 (2003), 1-26.