Bounding multiplicative energy by the sumset

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August undefined, 2024

WebMay 22, 2024 · We prove that the sumset or the productset of any finite set of real numbers, A, is at least A 4/3−ε, improving earlier bounds. Our main tool is a new upper bound on the multiplicative energy ... WebWe prove that the sumset or the productset of any finite set of real numbers, A, is at least A 4/3−ε, improving earlier bounds. Our main tool is a new upper bound on the multiplicative energy, E(A, A). 1. Keyphrases multiplicative energy new upper bound main tool

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WebApr 7, 2013 · P. Erdős and E. Szemerédi, “On sums and products of integers,” in Studies in Pure Mathematics (Birkhäuser, Basel, 1983), pp. 213–218.. Google Scholar . J. Solymosi, “Bounding multiplicative energy by the sumset,” Adv. Math. 222(2), 402–408 (2009). Article MathSciNet MATH Google Scholar WebJun 12, 2024 · Abstract. We give a construction of a set A \subset \mathbb N such that any subset {A' \subset A} with A' \gg A ^ {2/3} is neither an additive nor multiplicative … new outlaster codes

(PDF) Product of difference sets of set of primes - ResearchGate

WebOct 1, 2009 · We prove that the sumset or the productset of any finite set of real numbers, A, is at least A 4 / 3 − ε, improving earlier bounds. Our main tool is a new upper bound on the multiplicative energy, E ( A , A ) . http://www.numdam.org/item/JTNB_2024__31_3_573_0/ WebJul 12, 2016 · We prove that the sumset or the productset of any finite set of real numbers, A, is at least A 4/3−ε, improving earlier bounds. Our main tool is a new upper bound on the multiplicative energy ... new outlaw country bands

On the few products, many sums problem - Numdam

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WebBounding multiplicative energy by the sumset József Solymosi July 29, 2024 Abstract. We prove that the sumset or the productset of any finite set of real numbers, A, is at … WebBOUNDING MULTIPLICATIVE ENERGY BY THE SUMSET JOZSEF SOLYMOSI Abstract. We prove that the sumset or the productset of any nite set of real numbers, A; is at … new outlander release dateWebThe multiplicative energy, E(A,B),is given by E(A,B)= (a,b,c,d)∈A×B ×A×B ∃λ∈R: (a,b)=(λc,λd). In the proof of Lemma 2.3 we did not use the fact that A=B,the proof … new outlander usa

"WebOct 11, 2024 · The sum-product problem can also be studied for A ⊂ R, and indeed most contemporary work on the conjectured bound (1) uses geometric arguments that hold over the reals. The current best estimate... " - Bounding multiplicative energy by the sumset

Bounding multiplicative energy by the sumset

On sum sets of sets having small product set SpringerLink

WebApr 10, 2024 · 2005: The Energy Policy Act of 2015, authorized under sections 25D and 48 of the US tax code, first created the 30% tax credit for residential and commercial solar … WebOn higher energy decompositions and the sum–product phenomenon - Volume 167 Issue 3 ... Bounding multiplicative energy by the sumset. Adv. Math. 222 (2) ... Additive and multiplicative Sidon sets. Acta Mathematica Hungarica, Vol. 165, Issue. 2, p. 326. CrossRef; Google Scholar; Kerr, Bryce 2024.

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WebOur main tool is a new upper bound on the multiplicative energy, $E(A,A).$ We prove that the sumset or the productset of any finite set of real numbers, $A,$ is at least $ A ^{4/3 … WebDec 1, 2011 · Bounding multiplicative energy by the sumset J. Solymosi Mathematics 2009 162 Highly Influential PDF View 4 excerpts, references background and methods …

WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. We prove that the sumset or the productset of any finite set of real numbers, A, is at least … WebJun 3, 2011 · J. Solymosi, Bounding multiplicative energy by the sumset, Advances in Mathematics 222 (2009), 402–408. Article MathSciNet MATH Google Scholar Y. Stein, The total reducibility order of a polynomial in two variables, Israel Journal of Mathematics 68 (1989), 109–122.

WebMay 6, 2024 · We adapt the above energy bound to larger subgroups and obtain new bounds on gaps between elements in cosets of subgroups of order ... [41] József Solymosi Bounding multiplicative energy by the sumset, Adv. Math., Volume 222 (2009) no. 2, … WebJun 5, 2008 · An upper bound on the multiplicative energy Jozsef Solymosi We prove that the sumset or the productset of any finite set of real numbers, is at least improving earlier bounds. Our main tool is a new upper bound on the multiplicative energy, Submission history From: Jozsef Solymosi [ view email ] [v1] Thu, 5 Jun 2008 19:24:27 UTC (4 KB)

Web[14] J.Solymosi,Bounding multiplicative energy by the sumset,Adv.Math.(2009),doi:10.1016/ j.aim.2009.04.006 [15] G.Tenenbaum,Sur la probabilit´e qu’un entier poss`ede un diviseur dans un intervalle donn´e, CompositioMath.51 (1984),243–263. MR0739737(86c:11009) Department of Mathematics, Shanghai Jiao …

WebOct 22, 2015 · Abstract We improve the sum–product result of Solymosi in R; namely, we prove that max { A + A , AA } ****** A 4/3+c, where c > 0 is an absolute constant. New lower bounds for sums of sets with small product set are found. Previous results are improved effectively for sets A ⊂ R with AA ≤ A 4/3. new outlandersWebMay 22, 2012 · Bounding multiplicative energy by the sumset. Article. Oct 2009; Jozsef Solymosi; We prove that the sumset or the productset of any finite set of real numbers, A, is at least A 4/3−ε ... new outlander tv ss new outlander suvWebWe prove that the sumset or the productset of any finite set of real numbers, A, is at least A 4 / 3 − e , improving earlier bounds. Our main tool is a new upper bound on the … new outlaw country top songsWebLearn how to re-pot a root bound Peace Lily. Marie at Hall's Flower Shop and Garden Center in Stone Mountain GA shows us how easy it is to properly re-pot a... introduction\u0027s wcWebOct 5, 2014 · A bound on the multiplicative energy of a sum set and extremal sum-product problems Authors: Oliver Roche-Newton Dmitry Zhelezov University of … new outlander series 2021WebWe adapt the above energy bound to larger subgroups and obtain new bounds on gaps between elements in cosets of ... Shparlinski, Igor E. Multiplicative energy of shifted sugroups and bounds on exponential sums with trinomials in finite fields (2024) (https ... József Bounding multiplicative energy by the sumset, Adv. Math., Volume 222 ... new outlet application