Bounding multiplicative energy by the sumset
From MaRDI portal
Publication:838130
DOI10.1016/j.aim.2009.04.006zbMath1254.11016OpenAlexW2029408549WikidataQ57534457 ScholiaQ57534457MaRDI QIDQ838130
Publication date: 21 August 2009
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.aim.2009.04.006
Additive bases, including sumsets (11B13) Arithmetic combinatorics; higher degree uniformity (11B30)
Related Items
On sum sets and convex functions, If \(A + A\) is small then \(AAA\) is superquadratic, A note on Solymosi's sum-product estimate for ordered fields, On product of difference sets for sets of positive density, Sum-product theorems in algebraic number fields, The multiplication table problem for bipartite graphs, Elementary and combinatorial methods for counting prime numbers, On the energy variant of the sum-product conjecture, Few products, many h-fold sums, An update on the sum-product problem, On the growth rate in SL2(Fp)${\rm SL_2}(\mathbb {F}_p)$, the affine group and sum‐product type implications, On the number of distinct values of a class of functions with finite domain, Variations on the Sum-Product Problem II, Expansion for cubes in the Heisenberg group, An improved incidence bound for fields of prime order, On sum sets of sets having small product set, EXPANDING POLYNOMIALS ON SETS WITH FEW PRODUCTS, Sum-product phenomena for planar hypercomplex numbers, On the few products, many sums problem, Some remarks on the Balog-Wooley decomposition theorem and quantities \(D^+\), \(D^\times\), Some remarks on sets with small quotient set, On iterated product sets with shifts. II, On the size of the set AA+A, NEW RESULTS ON SUM‐PRODUCT TYPE GROWTH OVER FIELDS, The Szemerédi-Trotter type theorem and the sum-product estimate in finite fields, Another sum-product estimate in finite fields, On asymptotic formulae in some sum–product questions, Arithmetic combinatorics on Vinogradov systems, On Cartesian products which determine few distinct distances, A Szemerédi-Trotter type theorem, sum-product estimates in finite quasifields, and related results, On some applications of GCD sums to arithmetic combinatorics, On discrete values of bilinear forms, Fourier analysis and expanding phenomena in finite fields, New results on sums and products in \(\mathbb{R}\), On the number of incidences between points and planes in three dimensions, ON THREE-VARIABLE EXPANDERS OVER FINITE FIELDS, Sums and products with smooth numbers, Algebraic methods in sum-product phenomena, Sums and products along sparse graphs, Additive and multiplicative Sidon sets, On sums and products in \(\mathbb C[x\)], An application of kissing number in sum-product estimates, If (A+A)/(A+A) is small, then the ratio set is large, An improved bound on \((A+A)/(A+A)\), Counting spectral radii of matrices with positive entries, Conditional expanding bounds for two-variable functions over prime fields, Sum-product type estimates for subsets of finite valuation rings, New expander bounds from affine group energy, Unnamed Item, Some remarks on products of sets in the Heisenberg group and in the affine group, Difference sets are not multiplicatively closed, An Improved Sum-Product Bound for Quaternions, A sum-division estimate of reals, On products of shifts in arbitrary fields, Asymmetric estimates and the sum-product problems, Fp is locally like ℂ, Multiparameter Projection Theorems with Applications to Sums-Products and Finite Point Configurations in the Euclidean Setting, Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition, Generalized incidence theorems, homogeneous forms and sum-product estimates in finite fields, On higher energy decompositions and the sum–product phenomenon, Variations on the Sum-Product Problem, Growth in groups: ideas and perspectives, On growth in an abstract plane, New sum-product estimates for real and complex numbers, New sum-product type estimates over finite fields
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Sums and products from a finite set of real numbers
- A new proof of Szemerédi's theorem for arithmetic progressions of length four
- The Erdős-Szemerédi problem on sum set and product set
- Product set estimates for non-commutative groups
- Discriminants, resultants, and multidimensional determinants
- On the number of sums and products
- On sums and products of integers
- ON THE NUMBER OF SUMS AND PRODUCTS