On the property between theta functions and Dedekind’s function according to the changes in the value periods

Abstract

In the study, two relations between the Dedekind’s h-function and q - function were established by using characteristic values (e ,e ′) ≡ (0,0), (0,1)(mod2) for q -function according to 1/ 8 coefficient of period pair(u,t ). The transformations among the theta functions according to the periods have been given and a Jacobian style elliptic functions has been set up the theta function by the help of a defined function.