Additive Decompositions of Subgroups of Finite Fields

DOI10.1137/130924470zbMath1287.11120arXiv1301.2872OpenAlexW2079818597MaRDI QIDQ5408598

Igor E. Shparlinski

Publication date: 10 April 2014

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.2872

zbMATH Keywords

finite fieldscharacter sumsadditive combinatoricsadditive decompositions

Mathematics Subject Classification ID

Estimates on character sums (11L40) Inverse problems of additive number theory, including sumsets (11P70) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (14)

On multiplicative decompositions of polynomial sequences, I ⋮ Additive decompositions of sets with restricted prime factors ⋮ On additive decompositions of primitive elements in finite fields ⋮ On sumsets involving \(k\)th powers of finite fields ⋮ On a polynomial version of the sum-product problem for subgroups ⋮ On multiplicative decompositions of polynomial sequences, II ⋮ NEW RESULTS ON SUM‐PRODUCT TYPE GROWTH OVER FIELDS ⋮ Differences of subgroups in subgroups ⋮ A conjecture of Sárközy on quadratic residues ⋮ Counting additive decompositions of quadratic residues in finite fields ⋮ Intersections of shifts of multiplicative subgroups ⋮ Multiplicative decomposition of arithmetic progressions in prime fields ⋮ Any small multiplicative subgroup is not a sumset ⋮ Difference sets are not multiplicatively closed

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