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- W3092208230 abstract "Using GCD sums, we show that the set of the primes has small common multiplicative energy with an arbitrary exponentially big integer set $S$ and, in particular, size of any arithmetic progression in $S$ having the beginning at zero, is at most $O(log |S| cdot log log |S|)$. This result can be considered as an integer analogue of Vinogradov's question about the least quadratic non--residue. The proof rests on a certain repulsion property of the function $f(x)=log x$. Also, we consider the case of general $k$--convex functions $f$ and obtain a new incidence result for collections of the curves $y=f(x)+c$." @default.
- W3092208230 created "2020-10-15" @default.
- W3092208230 creator A5071151408 @default.
- W3092208230 date "2020-10-06" @default.
- W3092208230 modified "2023-09-27" @default.
- W3092208230 title "On some applications of GCD sums to Arithmetic Combinatorics" @default.
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