On the number of coprime integer pairs within a circle

Wenguang Zhai; Xiaodong Cao

Acta Arithmetica (1999)

  • Volume: 90, Issue: 1, page 1-16
  • ISSN: 0065-1036

How to cite

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Wenguang Zhai, and Xiaodong Cao. "On the number of coprime integer pairs within a circle." Acta Arithmetica 90.1 (1999): 1-16. <http://eudml.org/doc/207312>.

@article{WenguangZhai1999,
author = {Wenguang Zhai, Xiaodong Cao},
journal = {Acta Arithmetica},
keywords = {lattice points; circle; number of coprime integer pairs},
language = {eng},
number = {1},
pages = {1-16},
title = {On the number of coprime integer pairs within a circle},
url = {http://eudml.org/doc/207312},
volume = {90},
year = {1999},
}

TY - JOUR
AU - Wenguang Zhai
AU - Xiaodong Cao
TI - On the number of coprime integer pairs within a circle
JO - Acta Arithmetica
PY - 1999
VL - 90
IS - 1
SP - 1
EP - 16
LA - eng
KW - lattice points; circle; number of coprime integer pairs
UR - http://eudml.org/doc/207312
ER -

References

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  1. [1] R. C. Baker and G. Harman, Numbers with a large prime factor, Acta Arith. 73 (1995), 119-145. 
  2. [2] E. Bombieri and H. Iwaniec, On the order of ζ(1/2+it), Ann. Scuola Norm. Sup. Pisa 13 (1986), 449-472. Zbl0615.10047
  3. [3] E. Fouvry and H. Iwaniec, Exponential sums with monomials, J. Number Theory 33 (1989), 311-333. Zbl0687.10028
  4. [4] D. R. Heath-Brown, The Pjateckiĭ-Šapiro prime number theorem, ibid. 16 (1983), 242-266. Zbl0513.10042
  5. [5] D. Hensley, The number of lattice points within a contour and visible from the origin, Pacific J. Math. 166 (1994), 295-304. Zbl0849.11078
  6. [6] M. N. Huxley, Exponential sums and lattice points II, Proc. London Math. Soc. 66 (1993), 279-301. Zbl0820.11060
  7. [7] A. Ivić, The Riemann Zeta-function, Wiley, 1985. Zbl0556.10026
  8. [8] C. H. Jia, On the distribution of squarefree numbers (II), Sci. China Ser. A 8 (1992), 812-827. 
  9. [9] E. Krätzel, Lattice Points, Deutsch. Verlag Wiss., Berlin, 1988. 
  10. [10] S. H. Min, Methods of Number Theory, Science Press, Beijing, 1983 (in Chinese). 
  11. [11] W. G. Nowak, Primitive lattice points in rational ellipses and related arithmetical functions, Monatsh. Math. 106 (1988), 57-63. Zbl0678.10032
  12. [12] B. R. Srinivasan, The lattice point problem of many-dimensional hyperboloids II, Acta Arith. 8 (1963), 173-204. Zbl0118.28201

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