Text Let m be an integer with m≥ 2. For A⊆ Z m and n∈ Z m, let R 1 (A, n), R 2 (A, n), R 3
(A, n) denote the number of solutions of the equation a+ a′= n with ordered pairs (a, a′)∈ …

For any positive integer $ m $, let $\mathbb {Z} _ {m} $ be the set of residue classes modulo
$ m $. For $ A\subseteq\mathbb {Z} _ {m} $ and $\overline {n}\in\mathbb {Z} _ {m} $, let $ R …

For any positive integer m, let Z m be the set of residue classes modulo m. For A⊆ Z m and
n¯∈ Z m, let representation function RA (n¯) denote the number of solutions of the equation …

For any positive integer $ m $, let $\mathbb {Z} _ {m} $ be the set of residue classes modulo
$ m $. For $ A\subseteq\mathbb {Z} _ {m} $ and $\overline {n}\in\mathbb {Z} _ {m} $, let …

Let G be a finite abelian group, A a nonempty subset of G and h≥ 2 an integer. For g∈ G, let
RA, h (g) denote the number of solutions of the equation x1+···+ xh= g with xi∈ A for 1≤ i≤ …

Let G be a finite abelian group and A⊆ G. For n∈ G, denote by rA (n) the number of ordered
pairs (a1, a2)∈ A2 such that a1+ a2= n. Among other things, we prove that for any odd …

This thesis was devoted to the different properties of the additive representation functions
and related problems just like Sidon sequences, additive complement sets etc. We can say …