Revista Matemática Complutense

, Volume 23, Issue 2, pp 501–513 | Cite as

Some additive combinatorics problems in matrix rings

  • Ron Ferguson
  • Corneliu Hoffman
  • Florian Luca
  • Alina Ostafe
  • Igor E. Shparlinski
Article

Abstract

We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers.

Keywords

Matrices Finite fields Additive combinatorics 

Mathematics Subject Classification (2000)

11C20 11D79 11T23 

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Copyright information

© Revista Matemática Complutense 2010

Authors and Affiliations

  • Ron Ferguson
    • 1
  • Corneliu Hoffman
    • 2
  • Florian Luca
    • 3
  • Alina Ostafe
    • 4
  • Igor E. Shparlinski
    • 5
  1. 1.Department of MathematicsUniversity of VloraVloraAlbania
  2. 2.School of MathematicsUniversity of BirminghamBirminghamUK
  3. 3.Instituto de MatemáticasUNAMMichoacánMexico
  4. 4.Institut für MathematikUniversität ZürichZürichSwitzerland
  5. 5.Department of ComputingMacquarie UniversitySydneyAustralia

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