Primitive lattice points in convex planar domains

Martin N. Huxley; Werner Georg Nowak

Acta Arithmetica (1996)

  • Volume: 76, Issue: 3, page 271-283
  • ISSN: 0065-1036

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Martin N. Huxley, and Werner Georg Nowak. "Primitive lattice points in convex planar domains." Acta Arithmetica 76.3 (1996): 271-283. <http://eudml.org/doc/206899>.

@article{MartinN1996,
author = {Martin N. Huxley, Werner Georg Nowak},
journal = {Acta Arithmetica},
keywords = {primitive lattice points; Riemann Hypothesis; convex planar domains; number of primitive lattice points; Riemann hypothesis},
language = {eng},
number = {3},
pages = {271-283},
title = {Primitive lattice points in convex planar domains},
url = {http://eudml.org/doc/206899},
volume = {76},
year = {1996},
}

TY - JOUR
AU - Martin N. Huxley
AU - Werner Georg Nowak
TI - Primitive lattice points in convex planar domains
JO - Acta Arithmetica
PY - 1996
VL - 76
IS - 3
SP - 271
EP - 283
LA - eng
KW - primitive lattice points; Riemann Hypothesis; convex planar domains; number of primitive lattice points; Riemann hypothesis
UR - http://eudml.org/doc/206899
ER -

References

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  1. [1] T. M. Apostol, Introduction to Analytic Number Theory, Springer, New York, 1976. 
  2. [2] R. C. Baker, The square-free divisor problem, Quart. J. Math. Oxford 45 (1994), 269-277. Zbl0812.11053
  3. [3] J. L. Hafner, New omega theorems for two classical lattice point problems, Invent. Math. 63 (1981), 181-186. Zbl0458.10031
  4. [4] D. R. Heath-Brown, The Piatetski-Shapiro prime-number theorem, J. Number Theory 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] E. Hlawka, Über Integrale auf konvexen Körpern I, Monatsh. Math. 54 (1950), 1-36. 
  7. [7] E. Hlawka, Über Integrale auf konvexen Körpern II, Monatsh. Math. 54 (1950), 81-99. Zbl0036.30902
  8. [8] E. Hlawka, Über die Zetafunktion konvexer Körper, Monatsh. Math. 54 (1950), 100-107. Zbl0036.30903
  9. [9] M. N. Huxley, Exponential sums and lattice points II, Proc. London Math. Soc. 66 (1993), 279-301. Zbl0820.11060
  10. [10] M. N. Huxley, The mean lattice point discrepancy, Proc. Edinburgh Math. Soc. 38 (1995), 523-531. Zbl0845.11036
  11. [11] M. N. Huxley, Area, Lattice Points, and Exponential Sums, Oxford University Press, to appear. 
  12. [12] A. Ivić, The Riemann Zeta-function, Wiley, New York, 1985. Zbl0556.10026
  13. [13] I. Kátai, The number of lattice points in a circle, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 8 (1965), 39-60. Zbl0151.04401
  14. [14] E. Krätzel, Lattice Points, Deutsch. Verlag Wiss., Berlin, 1988. 
  15. [15] H. L. Montgomery and R. C. Vaughan, The distribution of squarefree numbers, in: Recent Progress in Analytic Number Theory, Proc. Durham Sympos. 1979, Vol. I, H. Halberstam and C. Hooley (eds.), Academic Press, London, 1981, 247-256. 
  16. [16] B. Z. Moroz, On the number of primitive lattice points in plane domains, Monatsh. Math. 99 (1985), 37-43. Zbl0551.10038
  17. [17] W. G. Nowak, An Ω-estimate for the lattice rest of a convex planar domain, Proc. Roy. Soc. Edinburgh Sect. A 100 (1985), 295-299. Zbl0582.10033
  18. [18] W. G. Nowak, On the average order of the lattice rest of a convex planar domain, Proc. Cambridge Philos. Soc. 98 (1985), 1-4. Zbl0552.10032
  19. [19] W. G. Nowak, Primitive lattice points in rational ellipses and related arithmetic functions, Monatsh. Math. 106 (1988), 57-63. Zbl0678.10032
  20. [20] W. G. Nowak and M. Schmeier, Conditional asymptotic formulae for a class of arithmetic functions, Proc. Amer. Math. Soc. 103 (1988), 713-717. Zbl0658.10052
  21. [21] K. Prachar, Primzahlverteilung, Springer, Berlin, 1957. 

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