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• W2964111809 endingPage "281" @default.
• W2964111809 startingPage "231" @default.
• W2964111809 abstract "In this paper we obtain a series of asymptotic formulae in the sum–product phenomena over the prime field $mathbb {F}_p$. In the proofs we use the usual incidence theorems in $mathbb {F}_p$, as well as the growth result in $mathrm {SL}_2 (mathbb {F}_p)$ due to Helfgott. Here are some of our applications: $bullet ~$ a new bound for the number of the solutions to the equation $(a_1-a_2) (a_3-a_4) = (a’_1-a’_2) (a’_3-a’_4)$, $a_i, a’_iin A$, $A$ is an arbitrary subset of $mathbb {F}_p$, $bullet ~$ a new effective bound for multilinear exponential sums of Bourgain, $bullet ~$ an asymptotic analogue of the Balog–Wooley decomposition theorem, $bullet ~$ growth of $p_1(b) + 1/(a+p_2 (b))$, where $a,b$ runs over two subsets of $mathbb {F}_p$, $p_1,p_2 in mathbb {F}_p [x]$ are two non–constant polynomials, $bullet ~$ new bounds for some exponential sums with multiplicative and additive characters." @default.
• W2964111809 created "2019-07-30" @default.
• W2964111809 creator A5071151408 @default.
• W2964111809 date "2018-11-29" @default.
• W2964111809 modified "2023-09-27" @default.
• W2964111809 title "On asymptotic formulae in some sum–product questions" @default.
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• W2964111809 doi "https://doi.org/10.1090/mosc/283" @default.
• W2964111809 hasPublicationYear "2018" @default.
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