✦ LIBER ✦
On a Theorem of J. E. Olson and an Application (Vanishing Sums in Finite Abelianp-Groups)
✍ Scribed by G. Troi; U. Zannier
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 180 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1071-5797
No coin nor oath required. For personal study only.
✦ Synopsis
Generalizing a theorem by J. E. Olson determining the Davenport's constant of a finite abelian p-group A, we prove that if S 1 , . . . , S k are given sets of integers satisfying suitable conditions and if g 1 , . . . , g k ʦ A, then a nontrivial vanishing sum of the form s 1 g 1 ϩ и и и ϩ s k g k , s i ʦ S i may be found. The result may be applied to the problem of finding polynomials in F p [x] having small degree and prescribed value set on F p .