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Exact value of the exponent of convergence of the singular integral in Tarry’s problem for homogeneous polynomials of degree \(n\) in two variables. (English. Russian original) Zbl 1511.11038

Izv. Math. 85, No. 2, 332-340 (2021); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 85, No. 2, 172-180 (2021).
Summary: I. Sh. Jabbarov [Math. Notes 105, No. 3, 359–365 (2019); translation from Mat. Zametki 105, No. 3, 375–382 (2019; Zbl 1434.11165)] 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 \(n\).

MSC:

11D72 Diophantine equations in many variables
11L99 Exponential sums and character sums
11B75 Other combinatorial number theory

Citations:

Zbl 1434.11165
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References:

[1] Jabbarov I. Sh. 2019 Convergence exponent of a special integral in the two-dimensional Tarry problem with homogeneous polynomial of degree 2 Mat. Zametki105 375-382 · Zbl 1434.11166 · doi:10.4213/mzm11988
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