Reducibility of cubic polynomials mod p

被引:0
|
作者
Ruppert, WM [1 ]
机构
[1] UNIV ERLANGEN NURNBERG,INST MATH,D-91054 ERLANGEN,GERMANY
关键词
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
It is shown that an absolutely irreducible homogeneous cubic polynomial f is an element of Z[x(0), x(1), x(2)] is also absolutely irreducible mod p if p > 1248H(6) where H is the height of f. Module a general number theoretic conjecture an example shows that the result is best possible. (C) 1996 Academic Press, Inc.
引用
收藏
页码:198 / 206
页数:9
相关论文
共 50 条
  • [41] CLASS NUMBERS OF CYCLIC CUBIC NUMBER FIELDS OF Q(P),P=1 MOD 3
    MONTOUCHET, MN
    [J]. PROCEEDINGS OF THE JAPAN ACADEMY, 1971, 47 (07): : 585 - +
  • [42] P-ADIC ROOT SEPARATION FOR QUADRATIC AND CUBIC POLYNOMIALS
    Pejkovic, Tomislav
    [J]. RAD HRVATSKE AKADEMIJE ZNANOSTI I UMJETNOSTI-MATEMATICKE ZNANOSTI, 2016, 20 (528): : 9 - 18
  • [43] CUBIC CHARACTER SUMS OF CUBIC POLYNOMIALS
    WRIGHT, DJ
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 100 (03) : 409 - 413
  • [44] POLYNOMIALS WHOSE REDUCIBILITY IS RELATED TO THE GOLDBACH CONJECTURE
    Borwein, Peter
    Choi, Kwok-Kwong Stephen
    Martin, Greg
    Samuels, Charles L.
    [J]. JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2012, 26 (01): : 33 - 63
  • [45] On the reducibility of cyclotomic polynomials over finite fields
    Harrison, Brett A.
    [J]. AMERICAN MATHEMATICAL MONTHLY, 2007, 114 (09): : 813 - 818
  • [46] ON THE ARITHMETIC OF ELLIPTIC CURVES RELATED TO THE REDUCIBILITY OF POLYNOMIALS
    Yatsuda, Takahiro
    [J]. JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2008, 11 (02): : 185 - 202
  • [47] Invariants of polynomials mod Frobenius powers
    Drescher, C.
    Shepler, A., V
    [J]. JOURNAL OF ALGEBRA, 2020, 556 : 908 - 935
  • [48] LEGENDRE POLYNOMIALS MOD-4
    ROBERT, A
    [J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1993, 316 (12): : 1235 - 1240
  • [49] On the bias of cubic polynomials
    David Kazhdan
    Tamar Ziegler
    [J]. Selecta Mathematica, 2018, 24 : 511 - 520
  • [50] On the bias of cubic polynomials
    Kazhdan, David
    Ziegler, Tamar
    [J]. SELECTA MATHEMATICA-NEW SERIES, 2018, 24 (01): : 511 - 520