### Abstract

Let ℙ_{q} be the finite field with q elements and let A denote the . ring of polynomials in one variable with coefficients in ℙ_{q}. Let P be a monic polynomial irreducible in A. We obtain a bound for the least degree of a monic polynomial irreducible in A (q odd) which is a quadratic non-residue modulo P. We also find a bound for the least degree of a monic polynomial irreducible . in A which is a primitive root modulo P.

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

Pages (from-to) | 647-652 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 126 |

Issue number | 3 |

Publication status | Published - 1998 Dec 1 |

### Fingerprint

### Keywords

- Primitive roots
- Quadratic non-residues
- Riemann Hypothesis

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

_{q},[T].

*Proceedings of the American Mathematical Society*,

*126*(3), 647-652.

**On certain character sums over ℙ _{q},[T].** / Hsu, Chih Nung.

Research output: Contribution to journal › Article

_{q},[T]',

*Proceedings of the American Mathematical Society*, vol. 126, no. 3, pp. 647-652.

_{q},[T]. Proceedings of the American Mathematical Society. 1998 Dec 1;126(3):647-652.

}

TY - JOUR

T1 - On certain character sums over ℙq,[T]

AU - Hsu, Chih Nung

PY - 1998/12/1

Y1 - 1998/12/1

N2 - Let ℙq be the finite field with q elements and let A denote the . ring of polynomials in one variable with coefficients in ℙq. Let P be a monic polynomial irreducible in A. We obtain a bound for the least degree of a monic polynomial irreducible in A (q odd) which is a quadratic non-residue modulo P. We also find a bound for the least degree of a monic polynomial irreducible . in A which is a primitive root modulo P.

AB - Let ℙq be the finite field with q elements and let A denote the . ring of polynomials in one variable with coefficients in ℙq. Let P be a monic polynomial irreducible in A. We obtain a bound for the least degree of a monic polynomial irreducible in A (q odd) which is a quadratic non-residue modulo P. We also find a bound for the least degree of a monic polynomial irreducible . in A which is a primitive root modulo P.

KW - Primitive roots

KW - Quadratic non-residues

KW - Riemann Hypothesis

UR - http://www.scopus.com/inward/record.url?scp=21944446130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21944446130&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21944446130

VL - 126

SP - 647

EP - 652

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -