This book emphasizes the role of symmetry and presents as many viewpoints as possible of an important phenomenon — the functional equation of the associated zeta-function. It starts from the basics before warping into the space of new interest; from the ground state to the excited state. For example, the celebrated Gauss quadratic reciprocity law is proved in four independent ways, which are in some way or other dependent on the functional equation. The proofs rest on finite fields, repres...

This book paves the way for a proper understanding of current and future issues on global warming, air pollution, depletion of natural resources, cyberattacks on smart grids, amongst others, by unifying various diverse disciplines of science to focus on a sustainable green society of the future.Readers will find applications of science described through the practical use of mobilities, in this case, the electric vehicles.The book could be used to teach and study on issues of global warming...

The aim of the book is to give a smooth analytic continuation from basic subjects including linear algebra, group theory, Hilbert space theory, etc. to number theory. With plenty of practical examples and worked-out exercises, and the scope ranging from these basic subjects made applicable to number-theoretic settings to advanced number theory, this book can then be read without tears. It will be of immense help to the reader to acquire basic sound skills in number theory and its applicati...