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Field Arithmetic
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Book Synopsis Field Arithmetic by : Michael D. Fried
Download or read book Field Arithmetic written by Michael D. Fried and published by Springer Science & Business Media. This book was released on 2005 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)?
Book Synopsis Field Arithmetic by : Michael D. Fried
Download or read book Field Arithmetic written by Michael D. Fried and published by Springer Science & Business Media. This book was released on 2008-04-09 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt: Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? The third edition improves the second edition in two ways: First it removes many typos and mathematical inaccuracies that occur in the second edition (in particular in the references). Secondly, the third edition reports on five open problems (out of thirtyfour open problems of the second edition) that have been partially or fully solved since that edition appeared in 2005.
Book Synopsis Basic Structures of Function Field Arithmetic by : David Goss
Download or read book Basic Structures of Function Field Arithmetic written by David Goss and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews:"The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field." MR 97i:11062
Book Synopsis Function Field Arithmetic by : Dinesh S. Thakur
Download or read book Function Field Arithmetic written by Dinesh S. Thakur and published by World Scientific. This book was released on 2004 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting open problems. While it covers many topics treated in 'Basic Structures of Function Field Arithmetic' by David Goss, it complements that book with the inclusion of recent developments as well as the treatment of new topics such as diophantine approximation, hypergeometric functions, modular forms, transcendence, automata and solitons. There is also new work on multizeta values and log-algebraicity. The author has included numerous worked-out examples. Many open problems, which can serve as good thesis problems, are discussed.
Book Synopsis Basic Structures of Function Field Arithmetic by : David Goss
Download or read book Basic Structures of Function Field Arithmetic written by David Goss and published by Springer Science & Business Media. This book was released on 1997-11-18 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews:"The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field." MR 97i:11062
Book Synopsis Hardware Implementation of Finite-Field Arithmetic by : Jean-Pierre Deschamps
Download or read book Hardware Implementation of Finite-Field Arithmetic written by Jean-Pierre Deschamps and published by McGraw Hill Professional. This book was released on 2009-01-14 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Implement Finite-Field Arithmetic in Specific Hardware (FPGA and ASIC) Master cutting-edge electronic circuit synthesis and design with help from this detailed guide. Hardware Implementation of Finite-Field Arithmetic describes algorithms and circuits for executing finite-field operations, including addition, subtraction, multiplication, squaring, exponentiation, and division. This comprehensive resource begins with an overview of mathematics, covering algebra, number theory, finite fields, and cryptography. The book then presents algorithms which can be executed and verified with actual input data. Logic schemes and VHDL models are described in such a way that the corresponding circuits can be easily simulated and synthesized. The book concludes with a real-world example of a finite-field application--elliptic-curve cryptography. This is an essential guide for hardware engineers involved in the development of embedded systems. Get detailed coverage of: Modulo m reduction Modulo m addition, subtraction, multiplication, and exponentiation Operations over GF(p) and GF(pm) Operations over the commutative ring Zp[x]/f(x) Operations over the binary field GF(2m) using normal, polynomial, dual, and triangular
Book Synopsis Arithmetic of Finite Fields by : M. Anwar Hasan
Download or read book Arithmetic of Finite Fields written by M. Anwar Hasan and published by Springer Science & Business Media. This book was released on 2010-06-17 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Workshop on the Arithmetic of Finite Fields, WAIFI 2010, held in Istanbul, Turkey, in June 2010. The 15 revised full papers presented were carefully reviewed and selected from 33 submissions. The papers are organized in topical sections on efficient finite field arithmetic, pseudo-random numbers and sequences, Boolean functions, functions, Equations and modular multiplication, finite field arithmetic for pairing based cryptography, and finite field, cryptography and coding.
Book Synopsis Arithmetic of Finite Fields by : Joachim von zur Gathen
Download or read book Arithmetic of Finite Fields written by Joachim von zur Gathen and published by Springer. This book was released on 2008-07-08 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Workshop on the Arithmetic of Finite Fields, WAIFI 2008, held in Siena, Italy, in July 2008. The 16 revised full papers presented were carefully reviewed and selected from 34 submissions. The papers are organized in topical sections on structures in finite fields, efficient finite field arithmetic, efficient implementation and architectures, classification and construction of mappings over finite fields, and codes and cryptography.
Download or read book Finite Fields written by Rudolf Lidl and published by Cambridge University Press. This book was released on 1997 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted entirely to the theory of finite fields.
Book Synopsis Arithmetic of Finite Fields by : Sihem Mesnager
Download or read book Arithmetic of Finite Fields written by Sihem Mesnager and published by Springer Nature. This book was released on 2023-01-10 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on the Arithmetic of Finite Field, WAIFI 2022, held in Chengdu, China, in August – September 2022. The 19 revised full papers and 3 invited talks presented were carefully reviewed and selected from 25 submissions. The papers are organized in topical sections: structures in finite fields; efficient finite field arithmetic; coding theory; cryptography; sequences.
Download or read book Field Theory written by Steven Roman and published by Springer. This book was released on 2013-12-20 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials - the Kummer theory.
Book Synopsis Arithmetic of Finite Fields by : Lilya Budaghyan
Download or read book Arithmetic of Finite Fields written by Lilya Budaghyan and published by Springer. This book was released on 2018-12-29 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-workshop proceedings of the 7th International Workshop on the Arithmetic of Finite Field, WAIFI 2018, held in Bergen, Norway, in June 2018. The 14 revised full papers and six invited talks presented were carefully reviewed and selected from 26 submissions. The papers are organized in topical sections on invited talks; elliptic curves; hardware implementations; arithmetic and applications of finite fields and cryptography.
Book Synopsis Function Field Arithmetic by : Dinesh S. Thakur
Download or read book Function Field Arithmetic written by Dinesh S. Thakur and published by World Scientific. This book was released on 2004 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an exposition of function field arithmetic withemphasis on recent developments concerning Drinfeld modules, thearithmetic of special values of transcendental functions (such as zetaand gamma functions and their interpolations), diophantineapproximation and related interesting open problems.
Book Synopsis Arithmetic Duality Theorems by : J. S. Milne
Download or read book Arithmetic Duality Theorems written by J. S. Milne and published by . This book was released on 1986 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.
Book Synopsis Number Theory in Function Fields by : Michael Rosen
Download or read book Number Theory in Function Fields written by Michael Rosen and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.
Book Synopsis Algebraic Function Fields and Codes by : Henning Stichtenoth
Download or read book Algebraic Function Fields and Codes written by Henning Stichtenoth and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.
Book Synopsis Field Arithmetic by : Michael D. Fried
Download or read book Field Arithmetic written by Michael D. Fried and published by . This book was released on 2014-01-15 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
