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Современные проблемы теории чисел
13 мая 2021 г. 12:45, г. Москва, ZOOM


On an application of higher energies to Sidon sets

И. Д. Шкредов

Математический институт им. В.А. Стеклова Российской академии наук, г. Москва



Аннотация: We show that for any finite set $A$ and an arbitrary $\varepsilon>0$ there is $k=k(\varepsilon)$ such that the higher energy $\mathrm{E}_{k}(A)$ is at most $|A|^{k+\varepsilon}$ unless $A$ has a very specific structure. As an application we obtain that any finite subset $A$ of the real numbers or the prime field either contains an additive Sidon-type subset of size $|A|^{1 / 2+c}$ or a multiplicative Sidon-type subset of size $|A|^{1 / 2+c}$.
Conference ID: 942 0186 5629 Password is a six-digit number, the first three digits of which form the number p + 44, and the last three digits are the number q + 63, where p, q is the largest pair of twin primes less than 1000

Язык доклада: английский

Website: https://mi-ras-ru.zoom.us/j/94201865629?pwd=aUlIbFBFelhFTjhnUnZtdTNFL1IvZz09


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