On the Multidimensional Tarry Problem for a Cubic Polynomial

Abstract

A new upper bound for the exponent of convergence of a special integral in the Tarry problem is obtained. The result is based on the representation of a special integral as a surface integral extended to the manifold of solutions of the system of equations of the Tarry problem. New estimates of the arising surface integrals reducing the estimation to the study of operators with discrete spectrum are obtained by using maximal minors.

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Acknowledgments

The author wishes to express gratitude to M. Korolev for his help in the work on this paper.

Funding

This work was supported by the Fund DFG-Russian Academy of Sciences, No. 000 RUS 113/572.

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Correspondence to I. Sh. Dzhabbarov.

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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 5, pp. 657–673.

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Dzhabbarov, I.S. On the Multidimensional Tarry Problem for a Cubic Polynomial. Math Notes 107, 713–726 (2020). https://doi.org/10.1134/S0001434620050028

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Keywords

  • surface integrals
  • trigonometric integrals
  • Gram determinant
  • algebraic varieties
  • implicit functions