Prym differentials on variable torus

In this paper are obtained new results by theory multiplicative functions and Prym differentials on variable tori. First are obtained analogues theorem about full sum residues for Prym differentials of every integer order on torus. As corollary are proved a reciprocity laws. All kinds of elementary Prym differentials of every integer order are constructed, which holomorphically depends from moduli tori and characters. Proved analogues Appell's formula decomposition for function with characters. Examined a vector bundles of Prym differentials of every integer order over product Teichmueller spaces for torus and groups of characters.