This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.
Natural numbers are the oldest human invention. This book describes their nature, laws, history and current status. It has seven chapters.
This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.
In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory.
It was accomplished by W. Sinnott in 1978 (see Sinnott [1]), over a hundred years after Kummer proved his result. We will prove the analogue of Theorem 16.3 in the case of cyclotomic function fields Kn, where m = P is a monic ...
Beyer , W. A. & Waterman , M. S. ( 1974 ) . Error analysis of a computation of Euler's constant and In 2 , Math . Comp . 28 , 599–604 . Bohr , H. ( 1910 ) . Bidrag til de Dirichlet'ske Rækkers theori , København : G. E. C. Gad ...
There are , however , useful accounts in most introductory works on number theory ; see , in particular , Cassels ' An introduction to Diophantine approximation ( Cambridge U.P. , 1957 ) , and the books of Niven and Zuckerman ( Wiley ...
Elements of Number Theory: Including an Introduction to Equations Over Finite Fields
A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind ...
Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner.
Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra.