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The Resource Topics in the Theory of Algebraic Function Fields, by Gabriel Daniel Villa Salvador, (electronic resource)
Topics in the Theory of Algebraic Function Fields, by Gabriel Daniel Villa Salvador, (electronic resource)
Resource Information
The item Topics in the Theory of Algebraic Function Fields, by Gabriel Daniel Villa Salvador, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Topics in the Theory of Algebraic Function Fields, by Gabriel Daniel Villa Salvador, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmeticalgebraic viewpoint to the study of function fields as part of the algebraic theory of numbers, where a function field of one variable is the analogue of a finite extension of Q, the field of rational numbers. The author does not ignore the geometricanalytic aspects of function fields, but leaves an indepth examination from this perspective to others. Key topics and features: * Contains an introductory chapter on algebraic and numerical antecedents, including transcendental extensions of fields, absolute values on Q, and Riemann surfaces * Focuses on the Riemann–Roch theorem, covering divisors, adeles or repartitions, Weil differentials, class partitions, and more * Includes chapters on extensions, automorphisms and Galois theory, congruence function fields, the Riemann Hypothesis, the Riemann–Hurwitz Formula, applications of function fields to cryptography, class field theory, cyclotomic function fields, and Drinfeld modules * Explains both the similarities and fundamental differences between function fields and number fields * Includes many exercises and examples to enhance understanding and motivate further study The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra. The book can serve as a text for a graduate course in number theory or an advanced graduate topics course. Alternatively, chapters 14 can serve as the base of an introductory undergraduate course for mathematics majors, while chapters 59 can support a second course for advanced undergraduates. Researchers interested in number theory, field theory, and their interactions will also find the work an excellent reference
 Language

 eng
 eng
 Edition
 1st ed. 2006.
 Extent
 1 online resource (657 p.)
 Note
 Description based upon print version of record
 Contents

 Algebraic and Numerical Antecedents
 Algebraic Function Fields of One Variable
 The RiemannRoch Theorem
 Examples
 Extensions and Galois Theory
 Congruence Function Fields
 The Riemann Hypothesis
 Constant and Separable Extensions
 The RiemannHurwitz Formula
 Cryptography and Function Fields
 to Class Field Theory
 Cyclotomic Function Fields
 Drinfeld Modules
 Automorphisms and Galois Theory
 Isbn
 9780817645151
 Label
 Topics in the Theory of Algebraic Function Fields
 Title
 Topics in the Theory of Algebraic Function Fields
 Statement of responsibility
 by Gabriel Daniel Villa Salvador
 Language

 eng
 eng
 Summary
 The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmeticalgebraic viewpoint to the study of function fields as part of the algebraic theory of numbers, where a function field of one variable is the analogue of a finite extension of Q, the field of rational numbers. The author does not ignore the geometricanalytic aspects of function fields, but leaves an indepth examination from this perspective to others. Key topics and features: * Contains an introductory chapter on algebraic and numerical antecedents, including transcendental extensions of fields, absolute values on Q, and Riemann surfaces * Focuses on the Riemann–Roch theorem, covering divisors, adeles or repartitions, Weil differentials, class partitions, and more * Includes chapters on extensions, automorphisms and Galois theory, congruence function fields, the Riemann Hypothesis, the Riemann–Hurwitz Formula, applications of function fields to cryptography, class field theory, cyclotomic function fields, and Drinfeld modules * Explains both the similarities and fundamental differences between function fields and number fields * Includes many exercises and examples to enhance understanding and motivate further study The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra. The book can serve as a text for a graduate course in number theory or an advanced graduate topics course. Alternatively, chapters 14 can serve as the base of an introductory undergraduate course for mathematics majors, while chapters 59 can support a second course for advanced undergraduates. Researchers interested in number theory, field theory, and their interactions will also find the work an excellent reference
 http://library.link/vocab/creatorName
 Villa Salvador, Gabriel Daniel
 Dewey number
 512.7
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 pM2SAgq1Kk
 Language note
 English
 LC call number
 QA241247.5
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Mathematics: Theory & Applications
 http://library.link/vocab/subjectName

 Number theory
 Functions of complex variables
 Geometry, algebraic
 Field theory (Physics)
 Global analysis (Mathematics)
 Algebra
 Number Theory
 Functions of a Complex Variable
 Algebraic Geometry
 Field Theory and Polynomials
 Analysis
 Commutative Rings and Algebras
 Label
 Topics in the Theory of Algebraic Function Fields, by Gabriel Daniel Villa Salvador, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents
 Algebraic and Numerical Antecedents  Algebraic Function Fields of One Variable  The RiemannRoch Theorem  Examples  Extensions and Galois Theory  Congruence Function Fields  The Riemann Hypothesis  Constant and Separable Extensions  The RiemannHurwitz Formula  Cryptography and Function Fields  to Class Field Theory  Cyclotomic Function Fields  Drinfeld Modules  Automorphisms and Galois Theory
 Dimensions
 unknown
 Edition
 1st ed. 2006.
 Extent
 1 online resource (657 p.)
 Form of item
 online
 Isbn
 9780817645151
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/0817645152
 Specific material designation
 remote
 System control number

 (CKB)1000000000492125
 (EBL)3062231
 (SSID)ssj0000320430
 (PQKBManifestationID)11256854
 (PQKBTitleCode)TC0000320430
 (PQKBWorkID)10247806
 (PQKB)10303432
 (DEHe213)9780817645151
 (MiAaPQ)EBC3062231
 (EXLCZ)991000000000492125
 Label
 Topics in the Theory of Algebraic Function Fields, by Gabriel Daniel Villa Salvador, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents
 Algebraic and Numerical Antecedents  Algebraic Function Fields of One Variable  The RiemannRoch Theorem  Examples  Extensions and Galois Theory  Congruence Function Fields  The Riemann Hypothesis  Constant and Separable Extensions  The RiemannHurwitz Formula  Cryptography and Function Fields  to Class Field Theory  Cyclotomic Function Fields  Drinfeld Modules  Automorphisms and Galois Theory
 Dimensions
 unknown
 Edition
 1st ed. 2006.
 Extent
 1 online resource (657 p.)
 Form of item
 online
 Isbn
 9780817645151
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/0817645152
 Specific material designation
 remote
 System control number

 (CKB)1000000000492125
 (EBL)3062231
 (SSID)ssj0000320430
 (PQKBManifestationID)11256854
 (PQKBTitleCode)TC0000320430
 (PQKBWorkID)10247806
 (PQKB)10303432
 (DEHe213)9780817645151
 (MiAaPQ)EBC3062231
 (EXLCZ)991000000000492125
Library Locations

Architecture LibraryBorrow itGould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US35.205706 97.445050



Chinese Literature Translation ArchiveBorrow it401 W. Brooks St., RM 414, Norman, OK, 73019, US35.207487 97.447906

Engineering LibraryBorrow itFelgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US35.205706 97.445050

Fine Arts LibraryBorrow itCatlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US35.210371 97.448244

Harry W. Bass Business History CollectionBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

John and Mary Nichols Rare Books and Special CollectionsBorrow it401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US35.207487 97.447906


Price College Digital LibraryBorrow itAdams Hall 102 307 West Brooks St., Norman, OK, 73019, US35.210371 97.448244

Western History CollectionsBorrow itMonnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US35.209584 97.445414
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/TopicsintheTheoryofAlgebraicFunction/aVq5BrsmFdQ/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/TopicsintheTheoryofAlgebraicFunction/aVq5BrsmFdQ/">Topics in the Theory of Algebraic Function Fields, by Gabriel Daniel Villa Salvador, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>