ADDITIVE DECOMPOSITIONS OF SUBGROUPS OF FINITE FIELDS

作者：Shparlinski Igor E^*

来源：SIAM Journal on Discrete Mathematics, 2013, 27(4): 1870-1879.

DOI：10.1137/130924470

• additive decompositions
• finite fields
• character sums
• additive combinatorics

We say that a set S is additively decomposed into two sets A and B if S = {a + b : a is an element of A, b is an element of 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 Sarkozy 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.

• 出版日期2013