Memoirs of the American Mathematical Society 1996; 75 pp; softcover Volume: 122 ISBN10: 0821804723 ISBN13: 9780821804728 List Price: US$42 Individual Members: US$25.20 Institutional Members: US$33.60 Order Code: MEMO/122/583
 In this book, the author studies the Dirichlet series whose coefficients are the number of orders of a quartic field with given indices. Nakagawa gives an explicit expression of the Dirichlet series. Using this expression, its analytic properties are deduced. He also presents an asymptotic formula for the number of orders in a quartic field with index less than a given positive number. Readership Graduate students and research mathematicians interested in number theory, specifically cubic and quartic extensions. Table of Contents  Introduction
 Preliminaries
 Type \(1111\)
 Types \(112\) and \(111^2\)
 Types \(22\), \(21^2\) and \(1^21^2\)
 Types \(13\) and \(11^3\)
 Types \(4\) and \(1^4\)
 Type \(2^2\)
 Proof of Theorem 1
 Bibliography
