ADDITIVE DECOMPOSITIONS OF SETS WITH RESTRICTED PRIME FACTORS

作者:Elsholtz Christian*; Harper Adam J
来源:Transactions of the American Mathematical Society, 2015, 367(10): 7403-7427.

摘要

We investigate sumset decompositions of quite general sets with restricted prime factors. We manage to handle certain sets, such as the smooth numbers, even though they have little sieve amenability, and conclude that these sets cannot be written as a ternary sumset. This proves a conjecture by Sarkozy. We also clean up and sharpen existing results on sumset decompositions of the prime numbers.

  • 出版日期2015-10