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OverviewIn this Tract Professor Moreno develops the theory of algebraic curves over finite fields, their zeta and L-functions, and, for the first time, the theory of algebraic geometric Goppa codes on algebraic curves. Amongst the applications considered are: the problem of counting the number of solutions of equations over finite fields; Bombieri's proof of the Reimann hypothesis for function fields, with consequences for the estimation of exponential sums in one variable; Goppa's theory of error-correcting codes constructed from linear systems on algebraic curves. There is also a new proof of the Tsfasman–Vladut–Zink theorem. The prerequisites needed to follow this book are few, and it can be used for graduate courses for mathematics students. Electrical engineers who need to understand the modern developments in the theory of error-correcting codes will also benefit from studying this work. Full Product DetailsAuthor: Carlos Moreno (City University of New York)Publisher: Cambridge University Press Imprint: Cambridge University Press (Virtual Publishing) Volume: 97 ISBN: 9780511608766ISBN 10: 0511608764 Publication Date: 05 August 2012 Audience: Professional and scholarly , Professional & Vocational Format: Undefined Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of Contents1. Algebraic curves and function fields; 2. The Riemann–Roch theorem; 3. Zeta functions; 4. Applications to exponential sums and zeta functions; 5. Applications to coding theory; Bibliography.Reviews' ... a careful and comprehensive guide to some of the most fascinating of plasma processes, a treatment that is both thorough and up-to-date.' The Observatory ...well written and has many interesting exercises. It could be used as a textbook for a nice course addressed to students with some background in algebra or number theory. Jose Felipe Voloch, Mathematical Reviews This book is well written and has many interesting exercises. It could be used as a textbook for a nice course addressed to students with some background in algebra or number theory. Jose Felipe Voloch, Mathematical Reviews ' ... a careful and comprehensive guide to some of the most fascinating of plasma processes, a treatment that is both thorough and up-to-date.' The Observatory Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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