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Graduate Texts in Mathematics #83
Introduction to Cyclotomic Fields
This text on a central area of number theory covers p-adic L-functions, class numbers, cyclotomic units, Fermat’s Last Theorem, and Iwasawa’s theory of Z_p-extensions. This edition contains a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture, as well as a chapter on other recent developments, such as primality testing via Jacobi sums and Sinnott’s proof of the vanishing of Iwasawa’s f-invariant.
- GenresMathematics
389 pages, Hardcover
First published April 1, 1982
22 people want to read
About the author
Lawrence C. Washington
11 books2 followersLawrence Clinton Washington (born 1951, Vermont) is an American mathematician, who specializes in number theory.
Washington studied at Johns Hopkins University, where in 1971 he received his B.A. and masters degree. In 1974 he earned his PhD at Princeton University under Kenkichi Iwasawa with thesis Class numbers and Z_p extensions.[1] He then became an assistant professor at Stanford University and from 1977 at the University of Maryland, where he became in 1981 an associate professor and in 1986 a professor. He held visiting positions at several institutions, including IHES (1980/81), Max-Planck-Institut für Mathematik (1984), the Institute for Advanced Study (1996), and MSRI (1986/87), as well as at the University of Perugia, Nankai University and the State University of Campinas.
Washington wrote a standard work on cyclotomic fields. He also worked on p-adic L-functions. He wrote a treatise with Allan Adler on their discovery of a connection between higher-dimensional analogues of magic squares and p-adic L-functions.[2] Washington has done important work on Iwasawa theory, Cohen-Lenstra heuristics, and elliptic curves and their applications to cryptography.
In Iwasawa theory he proved with Bruce Ferrero in 1979 a conjecture of Kenkichi Iwasawa, that the \mu-invariant vanishes for cyclotomic Zp-extensions of abelian number fields (Theorem of Ferrero-Washington).[3]
In 1979–1981 he was a Sloan Fellow.
(from Wikipedia)
Washington studied at Johns Hopkins University, where in 1971 he received his B.A. and masters degree. In 1974 he earned his PhD at Princeton University under Kenkichi Iwasawa with thesis Class numbers and Z_p extensions.[1] He then became an assistant professor at Stanford University and from 1977 at the University of Maryland, where he became in 1981 an associate professor and in 1986 a professor. He held visiting positions at several institutions, including IHES (1980/81), Max-Planck-Institut für Mathematik (1984), the Institute for Advanced Study (1996), and MSRI (1986/87), as well as at the University of Perugia, Nankai University and the State University of Campinas.
Washington wrote a standard work on cyclotomic fields. He also worked on p-adic L-functions. He wrote a treatise with Allan Adler on their discovery of a connection between higher-dimensional analogues of magic squares and p-adic L-functions.[2] Washington has done important work on Iwasawa theory, Cohen-Lenstra heuristics, and elliptic curves and their applications to cryptography.
In Iwasawa theory he proved with Bruce Ferrero in 1979 a conjecture of Kenkichi Iwasawa, that the \mu-invariant vanishes for cyclotomic Zp-extensions of abelian number fields (Theorem of Ferrero-Washington).[3]
In 1979–1981 he was a Sloan Fellow.
(from Wikipedia)
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Displaying 1 - 2 of 2 reviews
March 18, 2008
This book is not as important as the point that this book represents.
I was taking a number theory class from a professor who is one of the leading experts on Iwasawa Theory. This book is an introduction to Iwasawa Theory. So, I was google searching for stuff relating to the course and I found this book. All of the other books relating to the course had been checked out of the math library. So I checked out this book instead. It turned out to be really helpful, more helpful than the other books on number theory that people had checked out.
This really illustrates the point that it helps to try to figured out where your teacher is coming from.
I only used the first couple of sections of this book. The topics covered where algebraic number-theoretic properties of cyclotomic fields, and L-Series associated with those fields.
I was taking a number theory class from a professor who is one of the leading experts on Iwasawa Theory. This book is an introduction to Iwasawa Theory. So, I was google searching for stuff relating to the course and I found this book. All of the other books relating to the course had been checked out of the math library. So I checked out this book instead. It turned out to be really helpful, more helpful than the other books on number theory that people had checked out.
This really illustrates the point that it helps to try to figured out where your teacher is coming from.
I only used the first couple of sections of this book. The topics covered where algebraic number-theoretic properties of cyclotomic fields, and L-Series associated with those fields.
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March 21, 2014512.3 W318 1982
Displaying 1 - 2 of 2 reviews