Additive decompositions of subgroups of finite fields

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


We say that a set S is additively decomposed into two sets A and B if S = {a + b : a and A, b and B}. Here we study additive decompositions of multiplicative subgroups of finite fields. In particular, we give some improvements and generalizations of results of Dartyge and Sárközy on additive decompositions of quadratic residues and primitive roots modulo p. We use some new tools such as the Karatsuba bound of double character sums and some results from additive combinatorics.

Original languageEnglish
Pages (from-to)1870-1879
Number of pages10
JournalSIAM Journal on Discrete Mathematics
Issue number4
Publication statusPublished - 2013
Externally publishedYes


  • Additive combinatorics
  • Additive decompositions
  • Character sums
  • Finite fields


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