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Sets of Linear Forms Which Are Hard to Compute

Authors Michael Kaminski, Igor E. Shparlinski

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Author Details

Michael Kaminski
  • Department of Computer Science, Technion - Israel Institute of Technology, Haifa, Israel
Igor E. Shparlinski
  • School of Mathematics and Statistics, University of New South Wales, Sydney, Australia


The authors would like to thank Michel Waldschmidt for the suggestion to use the work of Sert [Alain Sert, 1999] in their argument.

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Michael Kaminski and Igor E. Shparlinski. Sets of Linear Forms Which Are Hard to Compute. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 66:1-66:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


We present a uniform description of sets of m linear forms in n variables over the field of rational numbers whose computation requires m(n - 1) additions. Our result is based on bounds on the height of the annihilating polynomials in the Perron theorem and an effective form of the Lindemann-Weierstrass theorem which is due to Sert (1999).

Subject Classification

ACM Subject Classification
  • Theory of computation → Algebraic complexity theory
  • Linear algorithms
  • additive complexity
  • effective Perron theorem
  • effective Lindemann-Weierstrass theorem


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