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Original Articles

A Generalization of a Theorem of Birch

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Pages 2640-2648 | Received 31 Aug 2007, Published online: 22 Jul 2009

REFERENCES

  • Artin , E. ( 1967 ). Algebraic Numbers and Algebraic Functions . New York : Gordon and Breach .
  • Birch , B. J. ( 1957 ). Homogeneous forms of odd degree in a large number of variables . Mathematika 4 : 102 – 105 .
  • Brauer , R. ( 1945 ). A note on systems of homogeneous algebraic equations . Bull. A.M.S. 51 : 749 – 755 .
  • Greenberg , M. J. ( 1969 ). Lectures on Forms in Many Variables . New York : W.A. Benjamin, Inc .
  • Leep , D. B. , Schmidt , W. M. ( 1983 ). Systems of homogeneous equations . Inventiones Mathematicae 71 : 539 – 549 .
  • Pfister , A. ( 1995 ). Quadratic Forms with Applications to Algebraic Geometry and Topology . London Mathematical Society Lecture Note Series . Vol. 217 . Cambridge University Press .
  • Vaughan , R. C. ( 1997 ). The Hardy-Littlewood Method. 2nd ed . Cambridge : Cambridge University Press .
  • Wooley , T. D. ( 1998 ). On the local solubility of diophantine systems . Compositio Mathematica 111 : 149 – 165 .
  • Communicated by A. Prestel.

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