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The problem of the number of zeros of an elliptic integral is semialgebraic

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Literature cited

  1. V. I. Arnol'd, A. N. Varchenko, and S. M. Gussein-Zade, Singularities of Differentiable Mappings [in Russian], Vol. 2, Nauka, Moscow (1985).

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  2. Progress in Science and Technology: Contemporary Problems in Mathematics [in Russian], Vol. 1, All-Union Institute of Scientific and Technical Information, Moscow (1985).

  3. G. S. Petrv, “Elliptic integrals and their stability,” Funkts. Anal. Prilozh.,20, No. 1, 46–49 (1986).

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  4. G. S. Petrov, “On the number of zeros of complete elliptic integrals,” Funkts. Anal. Prilozh.,18, No. 2, 73–74 (1984).

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Authors
  1. G. S. Petrov
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Additional information

Translated from Matematicheskie Zametki, Vol. 44, No. 3, pp. 393–401, September, 1988.

The author expresses his thanks to V. I. Arnol'd for his interest in this work and A. G. Khovanskii for helpful discussions and simplifications of the proofs.

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Petrov, G.S. The problem of the number of zeros of an elliptic integral is semialgebraic. Mathematical Notes of the Academy of Sciences of the USSR 44, 699–703 (1988). https://doi.org/10.1007/BF01159133

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  • DOI: https://doi.org/10.1007/BF01159133

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