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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. RAN. Ser. Mat., 2021 Volume 85, Issue 2, Pages 172–180 (Mi im9004)

Exact value of the exponent of convergence of the singular integral in Tarry's problem for homogeneous polynomials of degree $n$ in two variables

M. A. Chahkiev

Russian State Social University, Moscow

Abstract: Jabbarov [1] obtained the exact value of the exponent of convergence of the singular integral in Tarry's problem for homogeneous polynomials of degree $2$. We extend this result to the case of polynomials of degree $n$.

Keywords: oscillatory integrals, singular integral, Tarry's problem.

UDC: 517.5

MSC: 11D72, 11L99, 11B75

Received: 25.12.2019
Revised: 13.07.2020

DOI: 10.4213/im9004


 English version:
Izvestiya: Mathematics, 2021, 85:2, 332–340

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© Steklov Math. Inst. of RAS, 2024