Trigonometric Sums in Number Theory and Analysis

By G. Arkhipov, V. N. Chubarikov, Anatoliĭ Alekseevich Karat︠s︡uba. 2004

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Restriction of Fourier transforms to curves and related oscillatory integrals (2006, methodology): “The necessity of the condition p′ ≥ d(d+ 1)q/2 follows by scaling and the necessity of the condition 1 ≤ p pd follows from work by Arkhipov, Chubarikov and Karatsuba [1] (cf. also [24], [2] and [9]).”
Vinogradov's mean value theorem via efficient congruencing, II (2011, unknown): “Thus, the work of Arkhipov, Chubarikov and Karatsuba, and Parsell, on exponential sums in many variables (see [2] and [22], for example) may be improved in a manner no less dramatic than can be seen in the context of the version of Vinogradov’s mean value theorem described within this paper.”