Abstract
The equivalence of these two conjectures can even be put in the following sharper form : If N is any positive integer, Conjecture I is true for all n ≤ N if and only if Conjecture II is true for all n ≤ N and all real characters x . In one direction this is trivial, since λ(v) = (v|N*)forv= 1,2,…, N, where (x | y) denotes the Legendre- Jacobi symbol and N* denotes the smallest positive integer such that (p | N*) = - 1 for all primes p not exceeding N.
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