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Subspace Theorem

In: Pillars of Transcendental Number Theory

Author

Listed:
  • Saradha Natarajan

    (University of Mumbai, DAE Centre for Excellence in Basic Sciences)

  • Ravindranathan Thangadurai

    (Harish-Chandra Research Institute, Department of Mathematics)

Abstract

Subspace theorem is a multidimensional extension of Roth’s theorem developed by Schmidt in 1980. He introduced several new ideas, especially from the geometry of numbers. An important ingredient was the properties of successive minima. Since the proofs of his results are beyond the scope of this book, we limit ourselves to stating two versions of his results and derive Roth’s theorem. See Sect. 9.1. In Sect. 9.2, we present some classical approximation results derived from Dirichlet’s multidimensional theorem.

Suggested Citation

  • Saradha Natarajan & Ravindranathan Thangadurai, 2020. "Subspace Theorem," Springer Books, in: Pillars of Transcendental Number Theory, chapter 0, pages 155-170, Springer.
    • Handle: RePEc:spr:sprchp:978-981-15-4155-1_9
    DOI: 10.1007/978-981-15-4155-1_9
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