Diophantine approximation by cubes of primes and an almost prime
by
Angel Koumtchev Kumchev
University of South Carolina

Let a₁, ..., a_k be real numbers with a₁/a₂ irrational and consider the form

a1x13 + ... + akxk3 .

(1)

We will show that if k=4 almost all real numbers can be "well approximated" by the values taken by (1) when x₂, ..., x₄ are prime and x₁ is a P₆ (i.e. has at most 6 prime divisors). This will imply that in the case k=8 the values attained by (1) when x₁ is a P₆ and the remaining variables are prime are dense in R.

http://www.math.sc.edu/~koumtche/

Date received: March 17, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacu-03.