@article{LinfootOnAP,
title={On a problem in the additive theory of numbers},
author={E. H. Linfoot and C. J. A. Evelyn},
journal={Mathematische Zeitschrift},
volume={30},
pages={433-448}
}

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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences

1998

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… Expand