Devised in the 19th century, Gauss and Jacobi Sums are classical formulas that form the basis for contemporary research in many of today's sciences. This book offers readers a solid grounding on the origin of these abstract, general theories. Though the main focus is on Gauss and Jacobi, the book does explore other relevant formulas, including Cauchy.
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Develops the explicit evaluation of Gauss and Jacobi sums, and the application of these evaluations to the determination of other character sums, such as Jacobsthal, Eisenstein and Brewer sums, the determination of the number of solutions of congruences and residual difference sets, reciprocity laws.
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First Sentence:
We shall assume that the reader has a modest knowledge of the theory of finite fields, as found for example in Ireland and Rosen [1, Chapter 7]. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
generalized cyclotomic numbers, quintic residuacity, quintic residue, power residue difference sets, octic residue, quintic reciprocity, quartic residue, quartic character, quartic residuacity, prime ideal factorization, cubic residuacity, irreducible cyclic codes, rational quartic reciprocity law, rational reciprocity laws, cubic residue symbol, trinomial equations, cubic reciprocity, cubic nonresidue, period polynomial, quadratic partition, primary integers, inner sum vanishes, biquadratic reciprocity, cubic character, quadratic units Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof By Theorem, Proof Let, Definition Let, Proof First, Proof Write, Proof By Proposition, Example Take, Evaluation of Jacobi, Proof By Corollary, Proof Choose, Proof By Lemma, Proof Observe, Proof Set, Proof Suppose, Example Let, Proof Assume, Proof From Theorem, Proof Put, Properties of the Eisenstein, Xk-a Xk-b New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We shall assume that the reader has a modest knowledge of the theory of finite fields, as found for example in Ireland and Rosen [1, Chapter 7]. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
generalized cyclotomic numbers, quintic residuacity, quintic residue, power residue difference sets, octic residue, quintic reciprocity, quartic residue, quartic character, quartic residuacity, prime ideal factorization, cubic residuacity, irreducible cyclic codes, rational quartic reciprocity law, rational reciprocity laws, cubic residue symbol, trinomial equations, cubic reciprocity, cubic nonresidue, period polynomial, quadratic partition, primary integers, inner sum vanishes, biquadratic reciprocity, cubic character, quadratic units Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof By Theorem, Proof Let, Definition Let, Proof First, Proof Write, Proof By Proposition, Example Take, Evaluation of Jacobi, Proof By Corollary, Proof Choose, Proof By Lemma, Proof Observe, Proof Set, Proof Suppose, Example Let, Proof Assume, Proof From Theorem, Proof Put, Properties of the Eisenstein, Xk-a Xk-b New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 58
books:
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10
books
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- Number Theory by Helmut Hasse on 6 pages
- Finite Fields (Encyclopedia of Mathematics and its Applications) by Rudolf Lidl on 5 pages
- Number Theory: An approach through history from Hammurapi to Legendre by André Weil in Back Matter (1), Back Matter (2), and Back Matter (3)
- Special Functions (Encyclopedia of Mathematics and its Applications) by George E. Andrews in Back Matter (1), and Back Matter (2)
- Disquisitiones Arithmeticae by Carl F. Gauss in Front Matter, and Back Matter
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- An Invitation to Modern Number Theory by Steven J. Miller in Back Matter
- Theory of Differentiation: A Unified Theory of Differentiation Via New Derivate Theorems and New Derivatives (Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts) by Krishna M. Garg in Back Matter
- Elementary and Analytic Theory of Algebraic Numbers (Springer Monographs in Mathematics) by Wladyslaw Narkiewicz in Back Matter
- Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (Canadian Mathematical Society Series of Monographs and Advan) by Jonathan M. Borwein in Back Matter
- Selected Areas in Cryptography: 10th Annual International Workshop, SAC 2003, Ottawa, Canada, August 14-15, 2003, Revised Papers (Lecture Notes in Computer Science) by Mitsuru Matsui on page 40
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