Sums of the divisor and unitary divisor functions.
Sums of the form modulo a prime.
Sums of three cubes, II
Estimates are provided for sth moments of cubic smooth Weyl sums, when 4 ≤ s ≤ 8, by enhancing the author's iterative method that delivers estimates beyond classical convexity. As a consequence, an improved lower bound is presented for the number of integers not exceeding X that are represented as the sum of three cubes of natural numbers.
Sums of three cubes in three linked three-progressions.
Sums of three squares in certain Cayley rings
Sums of twelve squares
Sums of two k th powers.
Sums of two powers of linear forms
Sums of two relatively prime cubes
Sums of units in function fields II: The extension problem
Sums of values of a rational function
Sums of values of even functions
Sumsets avoiding squarefree integers
Sumsets containing long arithmetic progressions and powers of 2
Sumsets in quadratic residues
We describe all sets which represent the quadratic residues in the sense that R = A + A or R = A ⨣ A. Also, we consider the case of an approximate equality R ≈ A + A and R ≈ A ⨣ A and prove that A is then close to a perfect difference set.
Sumsets of finite Beatty sequences.
Sumsets of Sidon sets
1. Introduction. A Sidon set is a set A of integers with the property that all the sums a+b, a,b∈ A, a≤b are distinct. A Sidon set A⊂ [1,N] can have as many as (1+o(1))√N elements, hence N/2 sums. The distribution of these sums is far from arbitrary. Erdős, Sárközy and T. Sós [1,2] established several properties of these sumsets. Among other things, in [2] they prove that A + A cannot contain an interval longer than C√N, and give an example that is possible. In [1] they show that A + A contains...
Sum-sets of small upper density
Sumsets without powerful numbers
S-unit equations over number fields.