Jacob's ladders, $\zeta$-factorization and infinite set of metamorphosis of a multiform

Abstract

In this paper we use Jacob's ladders together with fundamental Hardy-Littlewood formula (1921) to prove the so-called $\zeta$-factorization formula on the critical line. Simultaneously, we obtain a set of control parameters of metamorphosis of a multiform connected with the Riemann-Siegel formula.