This article is cited in 1 paper

On the convergence of the improper integral of the three-dimensional Tarry problem for polynomials of degree $3$ with noncomplete high form

C. R. Abdullayev

Ganja State University

Abstract: 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 $k=4$, 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.

Keywords: Tarry problem, exponent of convergence, surface integrals, Gram determinant, implicit function

UDC: 511; 517

MSC: 11L03

DOI: 10.36535/2782-4438-2025-245-124-133