Integers Represented as a Sum of Primes and Powers of Two
Number Theory
2007-05-23 v2
Abstract
It is shown that every sufficiently large even integer is a sum of two primes and exactly 13 powers of 2. Under the Generalized Rieman Hypothesis one can replace 13 by 7. Unlike previous work on this problem, the proof avoids numerical calculations with explicit zero-free regions of Dirichlet L-functions. The argument uses a new technique to bound the measure of the set on which the exponential sum formed from powers of 2 is large.
Keywords
Cite
@article{arxiv.math/0201299,
title = {Integers Represented as a Sum of Primes and Powers of Two},
author = {D. R. Heath-Brown and J. -C. Puchta},
journal= {arXiv preprint arXiv:math/0201299},
year = {2007}
}
Comments
32 Pages; typos corrected