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2. Algebraic number theory [2016]
 Xianke, Zhang, author.
 Second Edition.  China : Higher Education Press ; Oxford, U.K. : Alpha Science International Ltd, [2016]
 Description
 Book — 1 volume (various pagings) : illustrations ; 24 cm
 Summary

 Foreword / Prerequisites / Fields and Rings / Noetherian Rings and Dedekind Domains / Prime Decompositions in Extensions / Valuation Theory and Completions / Local Fields and Applications / Global Fields: Class Numbers and Units / Quadratic Fields and Cyclotomic Fields / Analytical Theory and Characters / Idele and Class Field Theory / Algebraic Function Fields / Forms / Bibiography / Index.
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QA247 .X53 2016  Unknown 
 Baumgart, Oswald.
 Cham [Switzerland] ; New York : Birkhauser, c2015.
 Description
 Book — xiv, 172 p. : ill. ; 25 cm
 Summary

 Translator's Preface. Baumgart's Thesis. Introduction. First Part:
 1. From Fermat to Legendre.
 2. Gauss's Proof by Mathematical Induction.
 3. Proof by Reduction.
 4. Eisenstein's Proof using Complex Analysis.
 5. Proofs using Results from Cyclotomy.
 6. Proofs based on the Theory of Quadratic Forms.
 7. The Supplementary Laws.
 8. Algorithms for Determining the Quadratic Character. Second Part:
 9. Gauss's Proof by Induction.
 10. Proofs by Reduction.
 11. Eisenstein's Proofs using Complex Analysis.
 12. Proofs using Results from Cyclotomy.
 13. Proofs based on the Theory of Quadratic Forms. Final Comments. Proofs of the Quadratic Reciprocity Law. Author Index. Subject Index.
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QA242 .B45 2015  Unknown 
4. Algebraic theory of quadratic numbers [2013]
 Trifković, Mak, author.
 New York : Springer, 2013.
 Description
 Book — 1 online resource (xi, 197 pages) : illustrations Digital: text file.PDF.
 Summary

 Examples
 A Crash Course in Ring Theory
 Lattices
 Arithmetic in Q[[sq. root]D]
 The Ideal Class Group and the Geometry of Numbers
 Continued Fractions
 Quadratic Forms.
5. Algebraic number theory [2011]
 Mollin, Richard A., 1947
 2nd ed.  Boca Raton, FL : CRC Press, c2011.
 Description
 Book — xvi, 426 p. ; 26 cm.
 Summary

 Integral Domains, Ideals, and Unique Factorization Integral Domains Factorization Domains Ideals Noetherian and Principal Ideal Domains Dedekind Domains Algebraic Numbers and Number Fields Quadratic Fields Field Extensions Automorphisms, Fixed Points, and Galois Groups Norms and Traces Integral Bases and Discriminants Norms of Ideals Class Groups Binary Quadratic Forms Forms and Ideals Geometry of Numbers and the Ideal Class Group Units in Number Rings Dirichlet's Unit Theorem Applications: Equations and Sieves Prime Power Representation Bachet's Equation The Fermat Equation Factoring The Number Field Sieve Ideal Decomposition in Number Fields Inertia, Ramification, and Splitting of Prime Ideals The Different and Discriminant Ramification Galois Theory and Decomposition Kummer Extensions and ClassField Theory The KroneckerWeber Theorem An ApplicationPrimality Testing Reciprocity Laws Cubic Reciprocity The Biquadratic Reciprocity Law The Stickelberger Relation The Eisenstein Reciprocity Law Appendix A: Abstract Algebra Appendix B: Sequences and Series Appendix C: The Greek Alphabet Appendix D: Latin Phrases Bibliography Solutions to OddNumbered Exercises Index.
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QA247 .M63 2011  Unknown 
 Narkiewicz, Władysław.
 Third ed.  Berlin : Springer, 2004.
 Description
 Book — 1 online resource (xi, 712 pages) Digital: text file.PDF.
 Summary

 1. Dedekind Domains and Valuations. 2. Algebraic Numbers and Integers. 3. Units and Ideal Classes. 4. Extensions. 5. Padic Fields. 6. Applications of the Theory of Padic Fields. 7. Analytical Methods. 8. Abelian Fields. 9. Factorizations 9.1. 485Elementary Approach.
 Appendix I. Locally Compact Abelian Groups.
 Appendix II. Function Theory.
 Appendix III. Baker's Method. Problems. References. Author Index. List of Symbols.
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 Narkiewicz, Władysław.
 3rd ed., [rev. and extended ed.].  Berlin ; New York : Springer, c2004.
 Description
 Book — x, 708 p. ; 24 cm.
 Summary

 Dedekind Domains and Valuations. Algebraic Numbers and Integers. Units and Ideal Classes. Extensions. Padic Fields. Applications of the Theory of padic Fields. Analytical Methods. Abelian Fields. Factorizations.
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QA247 .N3335 2004  Available 
8. Introductory algebraic number theory [2004]
 Alaca, Şaban, 1964
 Cambridge, UK ; New York : Cambridge University Press, 2004.
 Description
 Book — xvii, 428 p. ; 26 cm.
 Summary

 Introduction
 1. Integral domains
 2. Euclidean domains
 3. Noetherian domains
 4. Elements integral over a domain
 5. Algebraic extensions of a field
 6. Algebraic number fields
 7. Integral bases
 8. Dedekind domains
 9. Norms of ideals
 10. Decomposing primes in a number field
 11. Units in real quadratic fields
 12. The ideal class group
 13. Dirichlet's unit theorem
 14. Applications to diophantine equations.
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QA247 .A43 2004  Available 
9. A brief guide to algebraic number theory [2001]
 SwinnertonDyer, H. P. F.
 Cambridge ; New York : Cambridge University Press, 2001.
 Description
 Book — ix, 146 p. ; 23 cm.
 Summary

 Preface
 1. Numbers and ideals
 2. Valuations
 3. Special fields
 4. Analytic methods
 5. Class field theory
 Appendix
 Exercises
 Suggested further reading.
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QA247 .S95 2001  Unknown 
10. Classical theory of algebraic numbers [2001]
 Ribenboim, Paulo.
 1st ed.  New York : Springer, c2001.
 Description
 Book — xxiv, 681 p. : ill. ; 24 cm.
 Summary

 Unique Factorization Domains, Ideals, Principal Ideal Domains. Commutative Fields. Residue Classes. Quadratic Residues. Algebraic Integers. Integral Basis, Discriminant. The Decomposition of Ideals. The Norm and Classes of Ideals. Estimates for the Discriminant. Units. Extension of Ideals. Algebraic Interlude. The Relative Trace, Norm, Discriminant and Different. The Decomposition of Prime Ideals in Galois Extensions. Complements and Miscellaneous Numerical Examples. Local Methods for Cyclotomic Fields. Bernoulli Numbers. Fermat's Last Theorem for Regular Prime Exponents. More on Cyclotomic Extensions. Characters and Gaussian Sums. ZetaFunctions and L Series. The Dedekind ZetaFunction. Primes in Arithmetic Progressions. The Frobenius Automorphism and the Splitting of Prime Ideals. Class Number of Quadratic Fields. Class Number of Cyclotomic Fields. Miscellaneous Results about the Class Number of Cyclotomic Field.
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QA247 .R465 2001  Unknown 
11. Algebraic number theory [1999]
 Algebraische zahlentheorie. English
 Neukirch, Jürgen, 1937
 Berlin ; New York : Springer, c1999.
 Description
 Book — xvii, 571 p. ; 25 cm.
 Summary

 Algebraic Integers. The Theory of Valuations. RiemannRoch Theory. Abstract Class Field Theory. Local Class Field Theory. Global Class Field Theory. Zeta Functions and Lseries. Bibliography. Index.
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QA247 .N51713 1999  Unknown 
12. Algebraic Number Theory [1997]
 Koch, H. (Hans)
 Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint : Springer, 1997.
 Description
 Book — 1 online resource (V, 280 pages)
 Summary

 Preface. Basic Number Theory. Class Field Theory. Galois Groups. Abelian Fields. Artin LFunctions and Galois Module Structure.
 Appendix 1: Fields, Domains and Complexes.
 Appendix 2: Quadratic Residues.
 Appendix 3: Locally Compact Groups.
 Appendix 4: Bernoulli Numbers. Tables. References. Author Index. Subject Index.
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13. Algebraic number theory [1997]
 Koch, Helmut, 1932
 Berlin ; Heidelberg ; New York : Springer, c1991.
 Description
 Book — [i], 269 p. : ill. ; 24 cm.
 Summary

 Preface. Basic Number Theory. Class Field Theory. Galois Groups. Abelian Fields. Artin LFunctions and Galois Module Structure.
 Appendix 1: Fields, Domains and Complexes.
 Appendix 2: Quadratic Residues.
 Appendix 3: Locally Compact Groups.
 Appendix 4: Bernoulli Numbers. Tables. References. Author Index. Subject Index.
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QA247 .K63 1997  Unknown 
14. Number theory II : algebraic number theory [1992]
 Teorii͡a chisel 2. English
 Berlin ; New York : SpringerVerlag, 1992.
 Description
 Book — 269 p.
 Summary

 Contents: H. Koch, Algebraic Number Fields.
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QA247 .T45513 1992  Available 
15. Algebraic number theory [1991]
 Fröhlich, A. (Albrecht), 1916
 Cambridge ; New York : Cambridge University Press, 1991.
 Description
 Book — xiv, 355 p. : ill. ; 24 cm.
 Summary

 Notation
 Introduction
 1. Algebraic foundations
 2. Dedekind domains
 3. Extensions
 4. Classgroups and units
 5. Fields of low degree
 6. Cyclotomic fields
 7. Diophantine equations
 8. Lfunctions
 Appendices
 Exercises
 Glossary of theorems
 Index.
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QA247 .F7577 1991  Unknown 
 Narkiewicz, Władysław.
 2nd ed., substantially rev. and extended.  Berlin ; New York : SpringerVerlag ; Warszawa : PWNPolish Scientific Publishers, c1990.
 Description
 Book — xiii, 746 p. ; 25 cm.
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QA247 .N3332 1990  Available 
17. An introduction to algebraic number theory [1990]
 Sūron josetsu. English
 Ono, Takashi.
 2nd ed.  New York : Plenum Press, c1990.
 Description
 Book — xi, 223 p. : ill. ; 24 cm.
 Online
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QA247 .O56 1990  Available 
18. Periods of Hecke characters [1988]
 Schappacher, Norbert.
 Berlin ; New York : SpringerVerlag, c1988.
 Description
 Book — xv, 160 p. ; 24 cm.
 Summary

 Contents: Algebraic Hecke Characters. Motives for Algebraic Hecke Characters. The Periods of Algebraic Hecke Characters. Elliptic Integrals and the gamma Function. Abelian Integrals with Complex Multiplication. Motives of CM Modular Forms. References. Alphabetical List of Symbols and Concepts.
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QA3 .L28 V.1301  Available 
19. Algebraic number theory [1987]
 Stewart, Ian.
 2nd ed.  London ; New York : Chapman and Hall, 1987.
 Description
 Book — xix, 262 p. : ill. ; 23 cm.
 Summary

This work develops the theory of algebraic numbers and shows how this may be applied to various questions in number theory, including a special case of Fermat's Last Theorem.
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QA247 .S76 1987  Available 
 Moroz, B. Z.
 Berlin ; New York : SpringerVerlag, c1986.
 Description
 Book — vii, 176 p. ; 25 cm.
SAL3 (offcampus storage)
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QA3 .L28 V.1205 1986  Available 
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