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Number of solutions in a box of a linear equation in an Abelian group

Volume 143 / 2016

Maciej Zakarczemny Colloquium Mathematicum 143 (2016), 17-22 MSC: Primary 11D79; Secondary 20K01. DOI: 10.4064/cm6145-12-2015 Published online: 3 December 2015

Abstract

For every finite Abelian group $\varGamma $ and for all $g,a_1,\ldots ,a_k\in \varGamma ,$ if there exists a solution of the equation $\sum _{i=1}^k a_ix_i = g$ in non-negative integers $x_i\le b_i,$ where $b_i$ are positive integers, then the number of such solutions is estimated from below in the best possible way.

Authors

  • Maciej ZakarczemnyInstitute of Mathematics
    Cracow University of Technology
    Warszawska 24
    31-155 Kraków, Poland
    e-mail

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