Abstract:
We obtain upper and lower bounds for the convergence exponent of the singular integral in the many-dimensional analogue of Tarry's problem on the asymptotics of the number of solutions of systems of Diophantine equations. In several cases we establish the exact values of the convergence exponent of the singular integral.
Citation:
M. A. Chahkiev, “On the convergence exponent of the singular integral in the multi-dimensional analogue of Tarry's problem”, Izv. Math., 67:2 (2003), 405–418
\Bibitem{Cha03}
\by M.~A.~Chahkiev
\paper On the convergence exponent of the singular integral in the multi-dimensional analogue of Tarry's problem
\jour Izv. Math.
\yr 2003
\vol 67
\issue 2
\pages 405--418
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\crossref{https://doi.org/10.1070/IM2003v067n02ABEH000432}
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Linking options:
https://www.mathnet.ru/eng/im432
https://doi.org/10.1070/IM2003v067n02ABEH000432
https://www.mathnet.ru/eng/im/v67/i2/p211
This publication is cited in the following 3 articles:
M. A. Chahkiev, “Exact value of the exponent of convergence of the singular integral in Tarry's problem for homogeneous polynomials of degree $n$ in two variables”, Izv. Math., 85:2 (2021), 332–340
I. Sh. Jabbarov, “Convergence Exponent of a Special Integral in the Two-Dimensional Tarry Problem with Homogeneous Polynomial of Degree 2”, Math. Notes, 105:3 (2019), 359–365
S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev, M. E. Changa, “Scientific Achievements of Anatolii Alekseevich Karatsuba”, Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S1–S22
Citation in format AMSBIB
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