On the few products, many sums problem

Thomas Brendan Murphy, Misha Rudnev, Ilya D. Shkredov, Yurii N. Shteinikov

Type: Preprint

Publication Date: 2017-12-01

Citations: 10

Locations

arXiv (Cornell University) - View

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Works That Cite This (10)

Action	Title	Year	Authors
+	Double exponential sums and congruences with intervals and exponential functions modulo a prime	2018	M. Z. Garaev
+	On popular sums and differences of sets with small products	2019	Konstantin Olmezov Aliaksei Semchankau Ilya D. Shkredov
+	If A + A is small then AAA is superquadratic	2019	Oliver Roche‐Newton Ilya D. Shkredov
+ PDF Chat	On higher energy decompositions and the sum–product phenomenon	2018	George Shakan
+	Double Character Sums with Intervals and Arbitrary Sets in Finite Fields	2018	Ilya D. Shkredov Igor E. Shparlinski
+	A Remark on Sets with Small Wiener Norm	2020	Ilya D. Shkredov
+ PDF Chat	A NEW SUM–PRODUCT ESTIMATE IN PRIME FIELDS	2019	Changhao Chen Bryce Kerr Ali Mohammadi
+	On a theorem of Hegyv\'{a}ri and Hennecart	2019	Dao Nguyen Van Anh Le Quang Ham Doowon Koh Thang Pham Lê Anh Vinh
+	On asymptotic formulae in some sum-product questions	2018	Ilya D. Shkredov
+	If $A+A$ is small then $AAA$ is superquadratic	2018	Oliver Roche‐Newton Ilya D. Shkredov

Works Cited by This (27)

Action	Title	Year	Authors
+	Some applications of W. Rudin's inequality to problems of combinatorial number theory	2010	Ilya D. Shkredov
+ PDF Chat	On the number of sums and products	1997	György Elekes
+	Some new inequalities in additive combinatorics	2012	Ilya D. Shkredov
+ PDF Chat	Congruences involving product of intervals and sets with small multiplicative doubling modulo a prime and applications	2016	Javier Cilleruelo M. Z. Garaev
+ PDF Chat	On the size of $k$-fold sum and product sets of integers	2003	Jean Bourgain Mei-Chu Chang
+ PDF Chat	On additive shifts of multiplicative subgroups	2012	Il'ya Vladimirovich Vyugin Ilya D. Shkredov
+	On exponential sums over multiplicative subgroups of medium size	2014	Ilya D. Shkredov
+ PDF Chat	New bounds for Gauss sums derived from KTH powers, and for Heilbronn's exponential sum	2000	D. R. Heath‐Brown
+	On the Order of Finitely Generated Subgroups of Q*(modp) and Divisors ofp−1	1996	Francesco Pappalardi
+	Bounding multiplicative energy by the sumset	2009	József Solymosi