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- Title
New upper bounds for the Davenport and for the Erdős-Ginzburg-Ziv constants.
- Authors
Chintamani, M.; Moriya, B.; Gao, W.; Paul, P.; Thangadurai, R.
- Abstract
Let G be a finite abelian group (written additively) of rank r with invariants n, n, . . . , n, where n is the exponent of G. In this paper, we prove an upper bound for the Davenport constant D( G) of G as follows; D( G) ≤ n + n + ( c(3) − 1) n + ( c(4) − 1) n + · · · + ( c( r) − 1) n + 1, where c( i) is the Alon-Dubiner constant, which depends only on the rank of the group $${{\mathbb Z}_{n_r}^i}$$. Also, we shall give an application of Davenport's constant to smooth numbers related to the Quadratic sieve.
- Subjects
ABELIAN groups; INVARIANTS (Mathematics); MATHEMATICAL constants; MATHEMATICAL functions; MATHEMATICS
- Publication
Archiv der Mathematik, 2012, Vol 98, Issue 2, p133
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-011-0345-z