Jacob's ladders and new $\zeta$-functionals and corresponding $\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\zeta$-pulses

In this paper we obtain some sum-variants of our first $\zeta$-equivalent of the Fermat-Wiles theorem. For example, on the Riemann hypothesis, we give a new type of $\zeta$-equivalent based on a sum of isolated rectangle-shaped signals (pulses).