Distribution of values of polynomial Fermat quotients

被引：12

作者：

Shparlinski, Igor E. ^{[2
]}

Winterhof, Arne ^{[1
]}

机构：

[1] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math, A-4040 Linz, Austria

[2] Macquarie Univ, Dept Comp, N Ryde, NSW 2109, Australia

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2013年 / 19卷 / 01期

基金：

澳大利亚研究理事会;

关键词：

Fermat quotients; Polynomials; Fixed points; Image size; Multiplicity of values; CHARACTER SUMS; VALUE SET; DIVISIBILITY;

D O I：

10.1016/j.ffa.2012.10.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let P be an irreducible polynomial of degree n over F-q. For A is an element of F-q[X] with gcd(A. P) = 1 the polynomial Fermat quotient q(P)(A) is defined by q(P)(A) equivalent to A(qn-1) - 1/P (mod P) and deg q(P)(A) < n. We study several properties of polynomial Fermat quotients including the number of fixed points, the image size, and multiplicity of values in the image. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：93 / 104

页数：12

共 14 条

[1]

[Anonymous], B AM MATH SOC

[2]

Bach E., 1996, ALGORITHMIC NUMBER T

[3]

Bourgain J, 2010, MICH MATH J, V59, P313

[4] Short character sums with Fermat quotients [J].

Chang, Mei-Chu .

ACTA ARITHMETICA, 2012, 152 (01) :23-38

[5]

Chen ZX, 2010, LECT NOTES COMPUT SC, V6087, P73, DOI 10.1007/978-3-642-13797-6_6

[6] On the p-divisibility of Fermat quotients [J].

Ernvall, R ;

Metsankyla, T .

MATHEMATICS OF COMPUTATION, 1997, 66 (219) :1353-1365

[7] ON THE KUMMER-MIRIMANOFF CONGRUENCES [J].

FOUCHE, WL .

QUARTERLY JOURNAL OF MATHEMATICS, 1986, 37 (147) :257-261

[8] Multiplicative character sums of Fermat quotients and pseudorandom sequences [J].

Gomez, Domingo ;

Winterhof, Arne .

PERIODICA MATHEMATICA HUNGARICA, 2012, 64 (02) :161-168

[9]

HeathBrown DR, 1996, PROG MATH, V139, P451

[10] PSEUDORANDOMNESS AND DYNAMICS OF FERMAT QUOTIENTS [J].

Ostafe, Alina ;

Shparlinski, Igor E. .

SIAM JOURNAL ON DISCRETE MATHEMATICS, 2011, 25 (01) :50-71

← 1 2 →