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• Root of unity
  ...''m'' less than ''n''. Any ''n''-th root of unity is a primitive ''d''-th root of unity for some ''d'' dividing ''n''. ...d]]s and [[finite field]]s (in the latter case every non-zero element is a root of unity).
  1 KB (197 words) - 22:01, 7 February 2009
• Root of unity/Definition
  94 bytes (14 words) - 22:03, 7 February 2009
• Root of unity/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Root of unity]]. Needs checking by a human.
  592 bytes (76 words) - 20:06, 11 January 2010

Page text matches

• Root of unity
  ...''m'' less than ''n''. Any ''n''-th root of unity is a primitive ''d''-th root of unity for some ''d'' dividing ''n''. ...d]]s and [[finite field]]s (in the latter case every non-zero element is a root of unity).
  1 KB (197 words) - 22:01, 7 February 2009
• Cyclotomic polynomial
  ...mic polynomial''' is a [[polynomial]] whose roots are a set of primitive [[root of unity|roots of unity]]. The ''n''-th cyclotomic polynomial, denoted by Φ<sub>'' For a positive integer ''n'', let ζ be a primitive ''n''-th root of unity: then
  1 KB (206 words) - 14:55, 11 December 2008
• Coprime/Related Articles
  {{r|Root of unity}}
  649 bytes (85 words) - 15:41, 11 January 2010
• Cyclotomic field
  ...] generated by [[root of unity|roots of unity]]. If ζ denotes an ''n''-th root of unity, then the ''n''-th cyclotomic field ''F'' is the [[field extension]] <math> As above, we take ζ to denote an ''n''-th root of unity. The [[maximal order]] of ''F'' is
  2 KB (342 words) - 12:52, 21 January 2009
• Place (disambiguation)
  {{rpl|Root of unity}}
  682 bytes (87 words) - 04:00, 26 September 2013
• Cyclotomic field/Related Articles
  {{r|Root of unity}}
  584 bytes (79 words) - 15:48, 11 January 2010
• Monogenic field
  ...field]]s: if <math>K = \mathbf{Q}(\zeta)</math> with <math>\zeta</math> a root of unity, then <math>O_K = \mathbf{Z}[\zeta]</math>.
  1 KB (208 words) - 16:47, 17 December 2008
• Cubic reciprocity
  is a complex [[cube root of unity]]. ...sidue symbol <math>\left(\frac{\alpha}{\pi}\right)_3</math> to be the cube root of unity (power of <math>\omega</math>) satisfying
  2 KB (319 words) - 15:45, 27 October 2008
• Root of unity/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Root of unity]]. Needs checking by a human.
  592 bytes (76 words) - 20:06, 11 January 2010
• Finite field/Related Articles
  {{r|Root of unity}}
  692 bytes (91 words) - 16:33, 11 January 2010
• Quadratic field/Related Articles
  {{r|Root of unity}}
  644 bytes (86 words) - 19:50, 11 January 2010
• Algebraic number/Related Articles
  {{r|root of unity}}
  887 bytes (126 words) - 02:29, 22 December 2008
• Cyclotomic polynomial/Related Articles
  {{r|root of unity}}
  864 bytes (139 words) - 14:58, 11 December 2008
• Dirichlet character
  ...N''), where φ is the Euler [[totient function]], the values of χ are all [[root of unity|roots of unity]]. We extend χ to a function on the positive integers by d
  2 KB (335 words) - 06:03, 15 June 2009
• Cubic equation/Proofs
  And the other two roots are found by multiplying by a cube root of unity.
  8 KB (1,339 words) - 11:08, 15 September 2009
• Polynomial/Related Articles
  {{r|Root of unity}}
  2 KB (206 words) - 19:38, 11 January 2010
• Quadratic field
  If ''d'' is negative, then the only units in the ring of integers are [[root of unity|roots of unity]]. If ''d'' is positive, the unit group has rank one, with
  3 KB (453 words) - 17:18, 6 February 2009
• Algebraic number field
  ...belian group]] with [[free rank]] ''r''+''s''-1 and torsion subgroup the [[root of unity|roots of unity]] in ''K''. A free generator of ''U'' is termed a ''fundame
  7 KB (1,077 words) - 17:18, 10 January 2009