Fourier Analysis on Number Fields

Valenza Robert J. Ramakrishnan Dinakar

ISBN 10: 147573087X / ISBN 13: 9781475730876

Editore: Springer, 2013

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Codice articolo 1897865534

Dati bibliografici

• Titolo: Fourier Analysis on Number Fields
• Editore: Springer
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 147573087X
• ISBN 13: 9781475730876
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

The general aim of this book is to provide a modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasizing harmonic analysis on topological groups. The more particular goal is to cover John Tate's visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries--technical prerequisites that are often foreign to the typical, more algebraically inclinded number theorist.

Contenuti

1 Topological Groups.- 2 Some Representation Theory.- 3 Duality for Locally Compact Abelian Groups.- 4 The Structure of Arithmetic Fields.- 5 Adeles, Ideles, and the Class Groups.- 6 A Quick Tour of Class Field Theory.- 7 Tate’s Thesis and Applications.- Appendices.- Appendix A: Normed Linear Spaces.- A.1 Finite-Dimensional Normed Linear Spaces.- A.2 The Weak Topology.- A.3 The Weak-Star Topology.- Appendix B: Dedekind Domains.- B.1 Basic Properties.- B.2 Extensions of Dedekind Domains.- References.