On a problem in the additive theory of numbers

  title={On a problem in the additive theory of numbers},
  author={E. H. Linfoot and C. J. A. Evelyn},
  journal={Mathematische Zeitschrift},
The exponential sum over squarefree integers
We give an upper bound for the exponential sum over squarefree integers. This establishes a conjecture by Br\"udern and Perelli.
Exponential sums and additive problems involving square-free numbers
Let r v (N) denote the number of representations of the integer N as a sum of v square-free numbers. We obtain unconditional and conditional bounds for the error term in the asymptotic formula for
Every integer can be written as a square plus a squarefree
  • J. Urroz
  • Mathematics
    Expositiones Mathematicae
  • 2021
Representation of an integer as the sum of a prime in arithmetic progression and a square-free integer
Uniformly for small $q$ and $(a,q)=1$, we obtain an estimate for the weighted number of ways a sufficiently large integer can be represented as the sum of a prime congruent to $a$ modulo $q$ and a
Renewal sequences and record chains related to multiple zeta sums
For the random interval partition of $[0,1]$ generated by the uniform stick-breaking scheme known as GEM$(1)$, let $u_k$ be the probability that the first $k$ intervals created by the stick-breaking
On the probability of co-primality of two natural numbers chosen at random (Who was the first to pose and solve this problem?)
The article attempts to demonstrate the rich history of one truly remarkable problem situated at the confluence of probability theory and theory of numbers - finding the probability of co-primality
Sums and differences of power-free numbers
We employ a generalised version of Heath-Brown's square sieve in order to establish an asymptotic estimate of the number of solutions $a, b \in \mathbb N$ to the equations $a+b=n$ and $a-b=n$, where
Moment estimates for exponential sums over k-free numbers
We investigate the size of L^p-integrals for exponential sums over k-free numbers and prove essentially tight bounds.
The First Years
On the exponential sum over k–free numbers
This paper is concerned with mean values of exponential sum generating functions over k–free numbers, and especially their L1–means. We also provide non–trivial estimates for the L1–means of such