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Given A ⊆ Zn, the A-weighted zero-sum constant CA is defined to be the smallest natural number k such that any sequence of k elements in Zn has an A-weighted zero-sum subsequence of consecutive terms. A sequence of length CA - 1 in Zn which does not have any A-weighted zero-sum subsequence of consecutive terms is called a C-extremal sequence for A. For n odd, let S(n) be the set of all units in Zn whose Jacobi symbol with respect to n is one. Given a prime divisor p of n, let L(n; p) be the set of all units Zn whose Jacobi symbol with respect to n is the same as their Legendre symbol with respect to p. We characterize the C-extremal sequences for S(n) and L(n; p). Given A = Zn, the A-weighted Davenport constant DA is defined to be the smallest natural number k such that any sequence of k elements in Zn has an A-weighted zero-sum subsequence. A sequence of length DA - 1 in Zn which does not have any A-weighted zero-sum subsequence is called a D-extremal sequence for A. We characterize the D-extremal sequences for S(n) and L(n; p). [ABSTRACT FROM AUTHOR]

For a finite abelian group (G , +) , the constant C (G) is defined to be the smallest natural number k such that any sequence in G having length k will have a subsequence of consecutive terms whose sum is zero. For a subset A of Z n , the constant C A (n) is the smallest natural number k such that any sequence in G having length k will have an A -weighted zero-sum subsequence of consecutive terms. We determine the value of C A (n) for some weight-sets A which are related to units in Z n. [ABSTRACT FROM AUTHOR]