On sums of Ramanujan sums
On sums of -units and linear recurrences
On sums of sequences of integers, I
On sums of seven cubes of almost primes
On Sums of Squares in etc
On sums of squares of Pell-Lucas numbers.
On sums of three squares
We address the question of when an integer in a totally real number field can be written as the sum of three squared integers from the field and more generally whether it can be represented by a positive definite integral ternary quadratic form over the field. In recent work with Piatetski-Shapiro and Sarnak we have shown that every sufficiently large totally positive square free integer is globally integrally represented if and only if it is so locally at all places, thus essentially resolving...
On sums of three squares
On Sums of Two Coprime k-th Powers.
On sums of two cubes: an Ω₊-estimate for the error term
The arithmetic function counts the number of ways to write a natural number n as a sum of two kth powers (k ≥ 2 fixed). The investigation of the asymptotic behaviour of the Dirichlet summatory function of leads in a natural way to a certain error term which is known to be in mean-square. In this article it is proved that as t → ∞. Furthermore, it is shown that a similar result would be true for every fixed k > 3 provided that a certain set of algebraic numbers contains a sufficiently...
On sums of two kth powers: a mean-square asymptotics over short intervals
On sums of two kth powers: an asymptotic formula for the mean square of the error term
On sums over primes
On sum-sets and product-sets of complex numbers
We give a simple argument that for any finite set of complex numbers , the size of the the sum-set, , or the product-set, , is always large.
On sumsets and spectral gaps
On S-unit equations in two unknowns.
On supercharacter theoretic generalizations of monomial groups and Artin's conjecture
We extend the notions of quasi-monomial groups and almost monomial groups in the framework of supercharacter theories, and we study their connection with Artin’s conjecture regarding the holomorphy of Artin -functions.
On superpseudoprimes
On Sylow 2-subgroups of K2OF for quadratic number fields F.
On symmetric and antisymmetric balanced binary sequences.