Geodesic
On the Multidimensional Tarry Problem for a Cubic Polynomial
Matematičeskie zametki, Tome 107 (2020) no. 5, pp. 657-673

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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.
Keywords: surface integrals, trigonometric integrals, Gram determinant, algebraic varieties, implicit functions. 
@article{MZM_2020_107_5_a1,
     author = {I. Sh. Dzhabbarov},
     title = {On the {Multidimensional} {Tarry} {Problem} for a {Cubic} {Polynomial}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {657--673},
     publisher = {mathdoc},
     volume = {107},
     number = {5},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_5_a1/}
}
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I. Sh. Dzhabbarov. On the Multidimensional Tarry Problem for a Cubic Polynomial. Matematičeskie zametki, Tome 107 (2020) no. 5, pp. 657-673. http://geodesic.mathdoc.fr/item/MZM_2020_107_5_a1/