Few sums, many products
By György Elekes Gy., Imre Z. Ruzsa. 2003
58 citations recorded by the source corpus.
Subfields: Computational Theory and Mathematics, Computer Graphics and Computer-Aided Design, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/7b4abeec0e312906b0d9f1fff54e6e2b35b5364d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
- Ilya D. Shkredov
- M. Rudnev
- Oliver Roche-Newton
- Brendan Murphy
- Giorgis Petridis
- József Solymosi
- Sophie Stevens
- Frank de Zeeuw
In Computer Graphics and Computer-Aided Design
- Ilya D. Shkredov
- Oliver Roche-Newton
- Brendan Murphy
- Giorgis Petridis
- József Solymosi
- M. Rudnev
- Sophie Stevens
In Discrete Mathematics and Combinatorics
- Ilya D. Shkredov
- M. Rudnev
- Oliver Roche-Newton
- Brendan Murphy
- Giorgis Petridis
- Sophie Stevens
- József Solymosi
- Frank de Zeeuw
Citations in the corpus
- NEW RESULTS ON SUM‐PRODUCT TYPE GROWTH OVER FIELDS (2017, methodology): “ in Fp is O(|A|2/logγ |A|) for some absolute constant γ < 1. Substituting above implies that for A = {1,..., √ p/3} ⊂ Fp, we have T(A) ≫ |A|4 logγ |A|. Over the reals, Elekes and Ruzsa observed in [12] that the Szemer´edi-Trotter point-line incidence theorem [54] implies T(A) ≪ |A|4 log|A|. Becau”
- New sum-product type estimates over finite fields (2014, methodology): “pe of this paper. The latter approach has been fruitful to establish quantitative sum-product inequalities in all ranges of |AA|,|A +A|. If F = R or C, Elekes and Elekes-Ruzsa – see respectively [9], [11] – showed that the following inequalities can be derived from the Szemer´edi-Trotter theorem: (1”
- On the Number of Sums and Products (2005, background): “Chang [2], and independently Elekes and Ruzsa [6], proved a similar bound if the sumset is at most c|A|.”