On the second smallest prime non-residue

被引：2

作者：

McGown, Kevin J. ^{[1
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

来源：

JOURNAL OF NUMBER THEORY | 2013年 / 133卷 / 04期

关键词：

Dirichlet character; Non-residues; Power residues; FIELDS;

D O I：

10.1016/j.jnt.2012.09.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let x be a non-principal Dirichlet character modulo a prime p. Let q(1) < q(2) denote the two smallest prime non-residues of chi. We give explicit upper bounds on q(2) that improve upon all known results. We also provide a good upper estimate on the product q(1)q(2) which has an upcoming application to the study of norm-Euclidean Galois fields. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1289 / 1299

页数：11

共 16 条

[1]

[Anonymous], 2012, Mosc. J. Comb. Number Theory

[2] On a problem of Dobrowolski and Williams and the Polya-Vinogradov inequality [J].

Bachman, G ;

Rachakonda, L .

RAMANUJAN JOURNAL, 2001, 5 (01) :65-71

[3] On the non existence of the Euclidean algorithm in certain quadratic number fields [J].

Brauer, A .

AMERICAN JOURNAL OF MATHEMATICS, 1940, 62 :697-716

[4] The smallest quadratic non-remainder. [J].

Brauer, A .

MATHEMATISCHE ZEITSCHRIFT, 1931, 33 :161-176

[5]

Burgess D.A., 1963, J LONDON MATH SOC, V38, P253

[6]

Burgess D. A., 1962, Proc. Lond. Math. Soc., V12, P179, DOI 10.1112/plms/s3-12.1.179

[7] A NOTE ON PRIME K-TH POWER NONRESIDUES [J].

HUDSON, RH .

MANUSCRIPTA MATHEMATICA, 1983, 42 (2-3) :285-288

[8] ON THE CONSTANT IN BURGESS' BOUND FOR THE NUMBER OF CONSECUTIVE RESIDUES OR NON-RESIDUES [J].

McGown, Kevin J. .

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2012, 46 (02) :273-284

[9] NORM-EUCLIDEAN CYCLIC FIELDS OF PRIME DEGREE [J].

McGown, Kevin J. .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2012, 8 (01) :227-254

[10]

Norton K.K., 1971, MEM AM MATH SOC, V106

← 1 2 →