A study of the Theta Functions Nullwert Forms with New Transformations

This book gathers three peer reviewed research articles in order to present a simple study of Theta Functions in their Nullwert forms. This study uses easy mathematical tools and presents new results about the continuity and the rationality of the Nullwert forms of Theta Functions. Furthermore, this book presents new demonstrated Transformations of the Nullwert forms of Theta-3 and Theta-4 Functions thanks to a demonstrated recurrence relation. We hope that the results of this book will be useful for the mathematicians future works about Theta Functions, Zeta Functions and the other related subjects. The new Transformations presented in this book can also be the first step towards a new complete study of Theta Functions in their complex forms.