### Abstract

We study the distribution of lattice points a + ib on the fixed circle a^{2} + b^{2} = n. Our results apply p.p. to the representable integers n, and we supply bounds for the discrepancy of the distribution, and for the maximum and minimum of the angles between consecutive points. As a corollary, we are able to show that when n is representable then it is almost surely representable with min(a, b) small, with an explicit bound.

Original language | English |
---|---|

Pages (from-to) | 87-94 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 200 |

Issue number | 1-3 |

Publication status | Published - Apr 6 1999 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*200*(1-3), 87-94.

**On the angular distribution of Gaussian integers with fixed norm.** / Erdős, P.; Hall, R. R.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 200, no. 1-3, pp. 87-94.

}

TY - JOUR

T1 - On the angular distribution of Gaussian integers with fixed norm

AU - Erdős, P.

AU - Hall, R. R.

PY - 1999/4/6

Y1 - 1999/4/6

N2 - We study the distribution of lattice points a + ib on the fixed circle a2 + b2 = n. Our results apply p.p. to the representable integers n, and we supply bounds for the discrepancy of the distribution, and for the maximum and minimum of the angles between consecutive points. As a corollary, we are able to show that when n is representable then it is almost surely representable with min(a, b) small, with an explicit bound.

AB - We study the distribution of lattice points a + ib on the fixed circle a2 + b2 = n. Our results apply p.p. to the representable integers n, and we supply bounds for the discrepancy of the distribution, and for the maximum and minimum of the angles between consecutive points. As a corollary, we are able to show that when n is representable then it is almost surely representable with min(a, b) small, with an explicit bound.

UR - http://www.scopus.com/inward/record.url?scp=0345778824&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0345778824&partnerID=8YFLogxK

M3 - Article

VL - 200

SP - 87

EP - 94

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -