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VIDEO LIBRARY |
Conference to the Memory of Anatoly Alekseevitch Karatsuba on Number theory and Applications
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Characters sums with additive convolutions I. D. Shkredovabc a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow c Lomonosov Moscow State University, Faculty of Mechanics and Mathematics |
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Abstract: Let M.-C. Chang obtained a nontrivial upper bound for the sum $$ \biggl|\sum_{a\in A,\, b\in B} \chi(a+b)\biggr|\,\ll_{K,\varepsilon}\,|A||B|\cdot p^{-\tau(K,\varepsilon)}, \qquad (1) $$ where Recently, B. Hanson considered an analog of sum (1) for three sets $$ \biggl|\sum_{a\in A,\, b\in B,\, c\in C} \chi(a+b+c)\biggr|\,=\, o_{\delta}\bigl(|A||B||C|\bigr). \qquad (2) $$ Using the almost periodicity lemma of Croot–Sisask as well as new results on sum-products, we refine both (1) and (2). Language: Russian and English |