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

Maciej Zakarczemny

Colloquium Mathematicae, Tome 144 (2016), p. 17-22 / Harvested from The Polish Digital Mathematics Library

Résumé

For every finite Abelian group Γ and for all $g, a ₁, . . ., a_{k} \in Γ$ , if there exists a solution of the equation $\sum_{i = 1}^{k} a_{i} x_{i} = g$ in non-negative integers $x_{i} \leq b_{i}$ , where $b_{i}$ are positive integers, then the number of such solutions is estimated from below in the best possible way.

Publié le : 2016-01-01

Zbl 06545374

EUDML-ID : urn:eudml:doc:283935

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6145-12-2015,
     author = {Maciej Zakarczemny},
     title = {Number of solutions in a box of a linear equation in an Abelian group},
     journal = {Colloquium Mathematicae},
     volume = {144},
     year = {2016},
     pages = {17-22},
     zbl = {06545374},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6145-12-2015}
}

Maciej Zakarczemny. Number of solutions in a box of a linear equation in an Abelian group. Colloquium Mathematicae, Tome 144 (2016) pp. 17-22. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6145-12-2015/