Mudgal, Akshat Unbounded expansion of polynomials and products. (English) Zbl 07932312 Math. Ann. 390, No. 1, 381-415 (2024). MSC: 11B13 11B30 11B83 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhelezov, Dmitrii; Pálvölgyi, Dömötör Query complexity and the polynomial Freiman-Ruzsa conjecture. (English) Zbl 07415205 Adv. Math. 392, Article ID 108043, 18 p. (2021). MSC: 11B30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hanson, Brandon; Roche-Newton, Oliver; Zhelezov, Dmitrii On iterated product sets with shifts. II. (English) Zbl 1492.11018 Algebra Number Theory 14, No. 8, 2239-2260 (2020). MSC: 11B30 11D72 11J87 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shakan, George On higher energy decompositions and the sum-product phenomenon. (English) Zbl 1468.11036 Math. Proc. Camb. Philos. Soc. 167, No. 3, 599-617 (2019). MSC: 11B13 11B30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hanson, Brandon; Roche-Newton, Oliver; Zhelezov, Dmitrii On iterated product sets with shifts. (English) Zbl 1445.11113 Mathematika 65, No. 4, 831-850 (2019). MSC: 11P70 11B30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bush, Albert; Croot, Ernie Few products, many \(h\)-fold sums. (English) Zbl 1407.11021 Int. J. Number Theory 14, No. 8, 2107-2128 (2018). MSC: 11B30 11B75 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shkredov, Ilya D. Some remarks on sets with small quotient set. (English. Russian original) Zbl 1430.11019 Sb. Math. 208, No. 12, 1854-1868 (2017); translation from Mat. Sb. 208, No. 12, 144-158 (2017). MSC: 11B30 11B75 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Roche-Newton, Oliver; Rudnev, Misha; Shkredov, Ilya D. New sum-product type estimates over finite fields. (English) Zbl 1412.11018 Adv. Math. 293, 589-605 (2016). MSC: 11B30 11T99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. Multiplicative congruences with variables from short intervals. (English) Zbl 1385.11002 J. Anal. Math. 124, 117-147 (2014). MSC: 11A07 11L05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Alon, Noga; Angel, Omer; Benjamini, Itai; Lubetzky, Eyal Sums and products along sparse graphs. (English) Zbl 1288.05124 Isr. J. Math. 188, 353-384 (2012). MSC: 05C25 11B30 05C70 05C75 05E15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Banks, William D.; Covert, David J. Sums and products with smooth numbers. (English) Zbl 1273.11044 J. Number Theory 131, No. 6, 985-993 (2011). Reviewer: Yong-Gao Chen (Nanjing) MSC: 11B75 11N25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Croot, Ernie; Hart, Derrick On sums and products in \(\mathbb C[x]\). (English) Zbl 1253.11014 Ramanujan J. 22, No. 1, 33-54 (2010). Reviewer: Weidong Gao (Tianjin) MSC: 11B30 11C08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bourgain, Jean; Chang, Mei-Chu Sum-product theorems in algebraic number fields. (English) Zbl 1246.11021 J. Anal. Math. 109, 253-277 (2009). Reviewer: Wolfgang A. Schmid (Palaiseau) MSC: 11B30 11R99 × Cite Format Result Cite Review PDF Full Text: DOI
Solymosi, József Bounding multiplicative energy by the sumset. (English) Zbl 1254.11016 Adv. Math. 222, No. 2, 402-408 (2009). Reviewer: Olof Sisask (London) MSC: 11B30 11B13 × Cite Format Result Cite Review PDF Full Text: DOI
Łaba, Izabella From harmonic analysis to arithmetic combinatorics. (English) Zbl 1160.11004 Bull. Am. Math. Soc., New Ser. 45, No. 1, 77-115 (2008). Reviewer: Tom Sanders (Cambridge) MSC: 11B25 11B75 11L07 28A75 28A78 42B15 42B20 42B25 52C10 × Cite Format Result Cite Review PDF Full Text: DOI
Chang, Mei-Chu A sum-product estimate in algebraic division algebras. (English) Zbl 1215.11018 Isr. J. Math. 150, 369-380 (2005). Reviewer: Olaf Ninnemann (Berlin) MSC: 11B75 × Cite Format Result Cite Review PDF Full Text: DOI
Solymosi, József On sum-sets and product-sets of complex numbers. (English) Zbl 1098.11018 J. Théor. Nombres Bordx. 17, No. 3, 921-924 (2005). Reviewer: László A. Székely (Columbia) MSC: 11B75 11B13 11B05 × Cite Format Result Cite Review PDF Full Text: DOI Numdam Numdam EuDML
Chang, Mei-Chu A sum–product theorem in semi-simple commutative Banach algebras. (English) Zbl 1079.11007 J. Funct. Anal. 212, No. 2, 399-430 (2004). Reviewer: Imre Z. Ruzsa (Budapest) MSC: 11B05 46J05 × Cite Format Result Cite Review PDF Full Text: DOI
Chang, Mei-Chu On sums and products of distinct numbers. (English) Zbl 1060.11012 J. Comb. Theory, Ser. A 105, No. 2, 349-354 (2004). Reviewer: Imre Z. Ruzsa (Budapest) MSC: 11B75 05D05 × Cite Format Result Cite Review PDF Full Text: DOI
Bourgain, Jean; Chang, Mei-Chu On the size of \(k\)-fold sum and product sets of integers. (English) Zbl 1034.05003 J. Am. Math. Soc. 17, No. 2, 473-497 (2004). MSC: 11B75 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bourgain, Jean; Chang, Mei-Chu On multiple sum and product sets of finite sets of integers. (English) Zbl 1113.11050 C. R., Math., Acad. Sci. Paris 337, No. 8, 499-503 (2003). MSC: 11L07 11T23 × Cite Format Result Cite Review PDF Full Text: DOI Link