Article
Licensed
Unlicensed Requires Authentication

Sum-Product Inequalities with Perturbation

  • EMAIL logo , , and
Published/Copyright: June 4, 2011
Become an author with De Gruyter Brill
Author Information Explore this Subject
Integers
From the journal Volume 11 Issue 3

Abstract

Let A be a set of n > n0(ε) positive real numbers, all at least 1 apart. We show that if δa,b and are arbitrary real numbers satisfying and , we have .

Keywords.: Sum-Product Inequalities; Additive Combinatorics; Sumsets
Received: 2009-09-15
Revised: 2009-04-30
Accepted: 2010-06-07
Published Online: 2011-06-04
Published in Print: 2011-June

© de Gruyter 2011

Articles in the same Issue

  1. Preface
  2. On the Intersections of Fibonacci, Pell, and Lucas Numbers
  3. Proving Balanced T2 and Q2 Identities Using Modular Forms
  4. Sum-Product Inequalities with Perturbation
  5. Power Totients with Almost Primes
  6. On the Sum of Reciprocals of Amicable Numbers
  7. Tromping Games: Tiling with Trominoes
  8. There are No Multiply-Perfect Fibonacci Numbers
  9. Large Zero-Free Subsets of ℤ/pℤ
https://doi.org/10.1515/integ.2011.023
Keywords for this article
Sum-Product Inequalities; Additive Combinatorics; Sumsets

Articles in the same Issue

  1. Preface
  2. On the Intersections of Fibonacci, Pell, and Lucas Numbers
  3. Proving Balanced T2 and Q2 Identities Using Modular Forms
  4. Sum-Product Inequalities with Perturbation
  5. Power Totients with Almost Primes
  6. On the Sum of Reciprocals of Amicable Numbers
  7. Tromping Games: Tiling with Trominoes
  8. There are No Multiply-Perfect Fibonacci Numbers
  9. Large Zero-Free Subsets of ℤ/pℤ
Downloaded on 9.4.2026 from https://www.degruyterbrill.com/document/doi/10.1515/integ.2011.023/html
Scroll to top button