# Beatty sequences and multiplicative number theory

Acta Arithmetica (1995)

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

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top## How to cite

topA. 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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- [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] 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] E. Hlawka, The Theory of Uniform Distribution, AB Academic Publishers, 1984. Zbl0563.10001
- [6] L.-K. Hua, Introduction to Number Theory, Springer, 1982.
- [7] S. Lang, Introduction to Diophantine Approximation, Addison-Wesley, 1966. Zbl0144.04005
- [8] H. A. Porta and K. B. Stolarsky, Wythoff pairs as semigroup invariants, Adv. in Math. 85 (1991), 69-82 Zbl0728.11035
- [9] S. Ramanujan, Some formulae in the analytic theory of numbers, Messenger of Math. 45 (1916), 81-84.
- [10] J. D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985), 183-216. Zbl0575.42003

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