A symmetrized lattice of 2n points in terms of an irrational real number α is considered in the unit square, as in the theorem of Davenport. If α is a quadratic irrational, the square of the L2 discrepancy is found to be c(α)logn+O(loglogn) for a computable positive constant d05961405d7be6fd8b901a2" title="Click to view the MathML source">c(α). For the golden ratio φ , the value yields the smallest L2 discrepancy of any sequence of explicitly constructed finite point sets in the unit square. If the partial quotients 45910b1b41215453eb2e" title="Click to view the MathML source">ak of α grow at most polynomially fast, the L2 discrepancy is found in terms of 45910b1b41215453eb2e" title="Click to view the MathML source">ak up to an explicitly bounded error term. It is also shown that certain generalized Dedekind sums can be approximated using the same methods. For a special generalized Dedekind sum with arguments a, b an asymptotic formula in terms of the partial quotients of is proved.