Beatty sequences and multiplicative number theory

A. G. Abercrombie

Acta Arithmetica (1995)

  • Volume: 70, Issue: 3, page 195-207
  • ISSN: 0065-1036

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A. G. Abercrombie. "Beatty sequences and multiplicative number theory." Acta Arithmetica 70.3 (1995): 195-207. <http://eudml.org/doc/206748>.

@article{A1995,
author = {A. G. Abercrombie},
journal = {Acta Arithmetica},
keywords = {Beatty sequences; divisor function; metric diophantine approximation; asymptotic behaviour; Vaaler's trigonometric polynomials},
language = {eng},
number = {3},
pages = {195-207},
title = {Beatty sequences and multiplicative number theory},
url = {http://eudml.org/doc/206748},
volume = {70},
year = {1995},
}

TY - JOUR
AU - A. G. Abercrombie
TI - Beatty sequences and multiplicative number theory
JO - Acta Arithmetica
PY - 1995
VL - 70
IS - 3
SP - 195
EP - 207
LA - eng
KW - Beatty sequences; divisor function; metric diophantine approximation; asymptotic behaviour; Vaaler's trigonometric polynomials
UR - http://eudml.org/doc/206748
ER -

References

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  1. [1] S. D. Chowla, Some problems of Diophantine approximation I, Math. Z. 33 (1931), 544-563. Zbl0001.32501
  2. [2] W. J. Ellison (with M. Mendès France), Les Nombres Premiers, Hermann, 1975. Zbl0313.10001
  3. [3] S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, London Math. Soc. Lecture Note Ser. 126, Cambridge University Press, 1991. Zbl0713.11001
  4. [4] D. R. Heath-Brown, The fourth power moment of the Riemann zeta function, Proc. London Math. Soc. (3) 38 (1979), 385-422. Zbl0403.10018
  5. [5] E. Hlawka, The Theory of Uniform Distribution, AB Academic Publishers, 1984. Zbl0563.10001
  6. [6] L.-K. Hua, Introduction to Number Theory, Springer, 1982. 
  7. [7] S. Lang, Introduction to Diophantine Approximation, Addison-Wesley, 1966. Zbl0144.04005
  8. [8] H. A. Porta and K. B. Stolarsky, Wythoff pairs as semigroup invariants, Adv. in Math. 85 (1991), 69-82 Zbl0728.11035
  9. [9] S. Ramanujan, Some formulae in the analytic theory of numbers, Messenger of Math. 45 (1916), 81-84. 
  10. [10] J. D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985), 183-216. Zbl0575.42003

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