Upper bounds on the formula size of symmetric Boolean functions

It is proved that complexity of implementation of the counting function of $n$ Boolean variables with binary formulae is at most $n^{3.03}$ and is at most $n^{4.47}$ with respect to DeMorgan formulae. Hence, the same bounds hold for the formula size of any threshold symmetric function of $n$ variables, particularly, for majority function. The following bounds are proved for the formula size of any symmetric Boolean function of $n$ variables: $n^{3.04}$ with respect to binary formulae and $n^{4.48}$ with respect to DeMorgan formulae. A proof is based on modular arithmetic.