New upper bounds for the Davenport and for the ErdAs-Ginzburg-Ziv constants

作者：Chintamani, M. N.^*; Moriya, B. K.; Gao, W. D.; Paul, P.; Thangadurai, R.

来源：ARCHIV DER MATHEMATIK, 2012, 98(2): 133-142.

DOI：10.1007/s00013-011-0345-z

• Finite abelian groups
• Davenport constant
• Lattice point problem

Let G be a finite abelian group (written additively) of rank r with invariants n (1), n (2), . . . , n (r) , where n (r) 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) a parts per thousand currency sign n (r) + n (r-1) + (c(3) - 1)n (r-2) + (c(4) - 1) n (r-3) + center dot center dot center dot + (c(r) - 1)n (1) + 1, where c(i) is the Alon-Dubiner constant, which depends only on the rank of the group Z(nr)(i). Also, we shall give an application of Davenport's constant to smooth numbers related to the Quadratic sieve.

• 出版日期2012-2
• 单位常州工学院; 南开大学