a sum through its maximum term.) The main difficulty is to bound a real function of several arguments from above. They show that their function has only one local maximum. We proceed by the same method, but substantial changes are necessary for $ k>3.$

First, we observe (cf. [@MITZ], Appendix C) that the function in question is $\le$ the [*infimum* ]{} with respect to certain other parameters. This is based on generating functions: If $f(x)=\sum c_kx^k$ then $c^k \le f(a)/a^k,\, a>0, c_i\ge 0$ (a method rarely used in the area, a notable exception is [@PUY].) Thus to bound the maximum from above we need to find suitable parameters and show that the value with respect to these parameters is less than the required upper bound . (This leads to involved, but elementary calculus. )

To make this approach work we need appropriate generating functions: $X=X_{a_1}+ \dots X_{a_{3^n}},$ where $X_{a_i}$ is the indicator random variable of the event that assignment $a_i$ makes the formula true. Then $X^2= \sum_a \sum_b \, X_aX_b.$ To get $E[X^2]$ we need to determine Prob$[X_aX_b=1].$ To this end we observe that the equation $x_1+ \dots + x_k=c$ which is true under $a$ is true exactly under those 