A01=Fuhuo Li
A01=Nianliang Wang
A01=Shigeru Kanemitsu
Arithmetic Functions
Author_Fuhuo Li
Author_Nianliang Wang
Author_Shigeru Kanemitsu
Category=PBH
Control Systems
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Functional Equation
Reciprocity Law
Zeta-Function
Product details
- ISBN 9789814425636
- Publication Date: 22 Jan 2013
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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, representation theory of nilpotent groups, reciprocity law for the Dedekind sums, and the translation formula for the theta-series, respectively. Likewise, for example, the Euler function is treated in several different places.One of the important principles of learning is to work with the material many times. This book presents many worked-out examples and exercises to enhance the reader's comprehension on the topics covered in an in-depth manner. This is done in a different setting each time such that the reader will always be challenged. For the keen reader, even browsing the text alone, without solving the exercises, will yield some knowledge and enjoyment.
