2 citations · 5 across the 11 of their papers we have counts for
12 papers
The Minimal Number of Three-Term Arithmetic Progressions Modulo a Prime Converges to a Limit
Ernie Croot
Given a density t in (0,1], and a prime p, let S be any subset of F_p having at least tp elements, and having the least number of three-term arithmetic progressions mod p among all…
Complexity of Inverting the Euler Function
Scott Contini, Ernie Croot, Igor Shparlinski
We present an algorithm to invert the Euler function . The algorithm, for a given , in polynomial time ``on average'', finds the set of all solutions to…
Long Arithmetic Progressions in Critical Sets
Ernie Croot
In this paper we prove: If 0 < d < 1, and p is a sufficiently large prime, then if S is a subset of Z/pZ having the least number of three-term arithmetic progressions among all sub…
Sums of the Form 1/x_1^k + ... + 1/x_n^k Modulo a Prime
Ernie Croot
We show that for every and integer , there exists an integer so that for all primes , and integers , there exist integers…
k-term Arithmetic Progressions in Sumsets
Ernie Croot
In this paper we give a very elementary proof that if A and B are subsets of {1,2,...,N}, each having at least 5N^{1 - (4(k-1))^{-1}} elements, then the sumset A+B has a k-term ari…
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…