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Polynomial normal forms for functions of κ-valued logics (for prime values of κ) are considered. A polynomial normal form modulo κ (p.n.f.) is the sum modulo κ of products of variables, or variables with one or several Post negations, taken with some coefficients. The length of a p.n.f. is the number of distinct terms that appear in the form with nonzero coefficients. If κ is a prime number, then each function of κ-valued logic may be represented by various p.n.f. The length of a function of κ-valued logic in the class of p.n.f. is the minimum length of a p.n.f. representing this function. The Shannon function L p.n.f.  κ  (n) of the length of functions of κ-valued logic in the class of p.n.f. is the maximum length of a function in the class of p.n.f. among all n-ary functions of κ-valued logic. In thiswork the order of growth of the Shannon function L p.n.f  κ  (n) is established (for prime values of κ):

On the length of functions of κ-valued logic in the class of polynomial normal forms modulo κ