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<p>In the paper, we show that the special integral of the Tarry problem with an incomplete polynomial in three variables of degree&#xa0;3 converges when <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k=4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation>, i.e., the convergence exponent does not exceed&#xa0;8. This result is obtained by a new method based on the examining the structure of the set of solutions for the system of equations for the Tarry problem. Unlike cases considered earlier, we examine the case where the highest form of the polynomial does not contain all independent variables.</p>

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ON THE CONVERGENCE OF THE IMPROPER INTEGRAL OF THE THREE-DIMENSIONAL TARRY PROBLEM FOR POLYNOMIALS OF DEGREE 3 WITH INCOMPLETE HIGH FORM

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • C. R. Abdullayev

摘要

In the paper, we show that the special integral of the Tarry problem with an incomplete polynomial in three variables of degree 3 converges when \(k=4\) k = 4 , i.e., the convergence exponent does not exceed 8. This result is obtained by a new method based on the examining the structure of the set of solutions for the system of equations for the Tarry problem. Unlike cases considered earlier, we examine the case where the highest form of the polynomial does not contain all independent variables.