2 citations · 5 across the 11 of their papers we have counts for
4 papers · 2 filters
A Combinatorial Method for Counting Smooth Numbers in Sets of Integers
Ernie Croot
In this paper we present a method for producing asymptotic estimates for the number of integers in a given S having only ``small'' prime factors. The conditions that need to be ver…
On a coloring conjecture about unit fractions
Ernest S. Croot
We prove an old conjecture of Erd{\H o}s and Graham on sums of unit fractions: There exists a constant such that if we -color the integers in , then there exists a…
A Structure Theorem for Positive Density Sets Having the Minimal Number of 3-term Arithmetic Progressions
Ernie Croot
Assuming the well-known conjecture that [x,x+x^t] contains a prime for t > 0 and x sufficiently large, we prove: For 0 < r < 1, there exists 0 < s < r < 1, 0 < d < 1, and infinitel…
Memory Efficient Arithmetic
Ernie Croot
In this paper we give an algorithm for computing the mth base-b digit (m=1 is the least significant digit) of an integer n (actually, it finds sharp approximations to n/b^m mod 1),…