Download Algebraic Number Theory (Cambridge Studies in Advanced by A. Fröhlich,M. J. Taylor PDF

By A. Fröhlich,M. J. Taylor

This publication originates from graduate classes given in Cambridge and London. It presents a brisk, thorough therapy of the principles of algebraic quantity conception, and builds on that to introduce extra complex principles. all through, the authors emphasise the systematic improvement of options for the specific calculation of the fundamental invariants, resembling earrings of integers, classification teams, and devices. in addition they mix, at every one degree of improvement, thought with particular computations and purposes, and supply motivation by way of classical number-theoretic difficulties. a few particular issues are integrated that may be taken care of at this point yet can often merely be present in examine monographs or unique papers, for example: module conception of Dedekind domain names; tame and wild ramifications; Gauss sequence and Gauss classes; binary quadratic types; and Brauer kinfolk. this is often the single textbook at this point which mixes fresh, sleek algebraic thoughts including a considerable mathematics content material. it will likely be quintessential for all training and would-be algebraic quantity theorists.

Show description

Read or Download Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) PDF

Similar number theory books

Number Theoretic Methods: Future Trends (Developments in Mathematics)

This quantity includes the complaints of the very winning moment China-Japan Seminar held in lizuka, Fukuoka, Japan, in the course of March 12-16, 2001 less than the help of the Japan Society for the advertising of technological know-how (JSPS) and the nationwide technology starting place of China (NSFC), and a few invited papers of eminent number-theorists who visited Japan in the course of 1999-2001 on the party of the convention on the study Institute of Mathematical Sciences (RIMS), Kyoto collage.

Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176) (Annals of Mathematics Studies)

Modular varieties are vastly vital in a number of parts of arithmetic, from quantity thought and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a customary instance, have deep mathematics importance. sooner than this booklet, the quickest recognized algorithms for computing those Fourier coefficients took exponential time, other than in a few exact situations.

Quadratic Forms, Linear Algebraic Groups, and Cohomology: 18 (Developments in Mathematics)

The invited papers gathered during this quantity tackle issues regarding the study of Raman Parimala (plenary speaker on the upcoming ICM 2010). those topics concentration totally on the interaction among algebra, quantity concept, and algebraic geometry. The integrated contributions conceal interesting examine in parts equivalent to box patching and an explanation of the Serre's Conjecture II for functionality fields of advanced surfaces.

Mathematical Bridges

Development bridges among classical effects and modern nonstandard difficulties, this hugely correct paintings embraces vital subject matters in research and algebra from a problem-solving point of view. The publication is established to aid the reader in formulating and proving conjectures, in addition to devising strategies to special mathematical difficulties by means of making connections among numerous techniques and concepts from diverse components of arithmetic.

Extra info for Algebraic Number Theory (Cambridge Studies in Advanced Mathematics)

Example text

Download PDF sample

Rated 4.75 of 5 – based on 30 votes