Diffraction from visible lattice points and kth power free integers

Discrete Mathematics

Volumn 221, Issue 1-3, 2000, Pages 3-42

  Baake, Michael ^a   Moody, Robert V ^b   Pleasants, Peter A B ^c  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b UNIVERSITY OF ALBERTA   (Canada)

^c UNIVERSITY OF THE SOUTH PACIFIC   (Fiji)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011973787     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(99)00384-2     Document Type: Article

References (31)

1. T.M. Apostol, Introduction to Analytic Number Theory, Springer, New York, 1976.
2. L. Argabright, J. Gil de Lamadrid, Fourier Analysis of Unbounded Measures on locally Compact Abelian groups, Memoirs of the American Mathematical Society, Vol. 145, AMS, Providence, RI, 1974.
3. M. Baake, U. Grimm, D.H. Warrington, Some remarks on the visible points of a lattice, J. Phys. A 27 (1994) 2669-2674 and 5041 (Erratum); see also math-ph/9903046.
4. S.K. Berberian, Measure and Integration, Macmillan, New York, 1965, reprint: Chelsea, New York, 1970.
5. D. Berend, in preparation.
6. J.W.S. Cassels, Global Fields, in: J.W.S. Cassels, A. Fröhlich (Eds.), Algebraic Number Theory, Academic Press, London, 1967, pp. 42-84.
7. J.M. Cowley, Diffraction Physics, 3rd Edition, North-Holland, Amsterdam, 1995.
8. J. Dieudonné, Treatise on Analysis, Vol. II, Academic Press, New York, 1970.
9. G. Grimmett, Large deviations in the random sieve, Math. Proc. Cambridge Philos. Soc. 121 (1997) 519-530.
10. P.M. Gruber, C.G. Lekkerkerker, Geometry of Numbers, 2nd Edition, North-Holland, Amsterdam, 1987.
11. E. Hewitt, K.A. Ross, Abstract Harmonic Analysis I, 2nd Edition, Springer, New York, 1979.
12. A. Hof, On diffraction by aperiodic structures, Comm. Math. Phys. 169 (1995) 25-43.
13. A. Hof, Diffraction by aperiodic structures, in: R.V. Moody (Ed.), The Mathematics of Long-Range Aperiodic Order, NATO ASI Series C, Vol. 489, Kluwer, Dordrecht, 1997, pp. 239-268.
14. L.K. Hua, Introduction to Number Theory, Springer, Berlin, 1982.
15. M.N. Huxley, Moments of differences between square-free numbers, in: G.R.H. Greaves, G. Harman, M.N. Huxley (Eds.), Sieve Methods, Exponential Sums, and their Applications in Number Theory, Lecture Notes in Mathematics, Vol. 237, Cambridge University Press, Cambridge, 1997, pp. 187-204.
16. J.T. Knight, Commutative Algebra, Cambridge University Press, Cambridge, 1971.
17. J.C. Lagarias, Meyer's concept of quasicrystal and quasiregular sets, Comm. Math. Phys. 179 (1996) 365-376.
18. Y. Meyer, Algebraic Numbers and Harmonic Analysis, North-Holland, Amsterdam, 1972.
19. L. Mirsky, Arithmetical pattern problem relating to divisibility by rth powers, Proc. London Math. Soc. 50 (1949) 497-508.
20. R.V. Moody, Meyer sets and their duals, in: R.V. Moody (Eds.), The Mathematics of Long-Range Aperiodic Order, NATO ASI Series C, Vol. 489, Kluwer, Dordrecht, 1997, pp. 403-441.
21. R. Mosseri, Visible points in a lattice, J. Phys. A 25 (1992) L25-L29.
22. S.S. Pillai, On sets of square-free numbers, J. Indian Math. Soc. (New Ser.) 2 (1936) 116-118.
23. P.A.B. Pleasants, in preparation.
24. M. Reed, B. Simon, Methods of Modern Mathematical Physics. I: Functional Analysis, 2nd Edition, Academic Press, San Diego, 1980.
25. W. Rudin, Functional Analysis, 2nd Edition, McGraw-Hill, New York, 1991.
26. D. Ruelle, Statistical Mechanics: Rigorous Results, Benjamin, Reading, 1969; reprint: Addison-Wesley, Redwood City, 1989.
27. M. Schlottmann, Cut-and-project sets in locally compact Abelian groups, in: J. Patera (Ed.), Quasicrystals and Discrete Geometry, Fields Institute Monographs, Vol. 10, AMS, Providence, RI, 1998, pp. 247-264.
28. M. Schlottmann, Generalized model sets and dynamical systems, in: M. Baake, R.V. Moody (Eds.), Directions in Mathematical Quasicrystals, CRM Monograph Series, AMS, Providence, RI, 2000, in press.
29. M.R. Schroeder, A simple function and its Fourier transform, Math. Intelligencer 4 (1982) 158-161, and: Number Theory in Science and Communication, 3rd Edition, Springer, Berlin, 1997.
30. M.R. Schroeder, A simple function and its Fourier transform, Math. Intelligencer 4 (1982) 158-161, and: Number Theory in Science and Communication, 3rd Edition, Springer, Berlin, 1997.
31. L. Schwartz, Théorie des Distributions, 3rd Edition, Hermann, Paris, 1998.