Holdings: A course in arithmetic

A course in arithmetic:

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Bibliographic Details
Main Author:	Serre, Jean-Pierre 1926- (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Springer [2001]
Edition:	6. printing
Series:	Graduate texts in mathematics 7
Subjects:	Algebraische Zahlentheorie Analytische Zahlentheorie Zahlkörper Arithmetik Zahlentheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	VIII, 115 S. graph. Darst.
ISBN:	3540900403 0387900403

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Record in the Search Index

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adam_text	Table of Contents Preface v Part I—Algebraic Methods Chapter /—Finite fields 3 1— Generalities 3 2— Equations over a finite field 5 3— Quadratic reciprocity law 6 Appendix — Another proof of the quadratic reciprocity law 9 Chapter Il—p-adk fields 1 j 1— The ring Zp and the field Qp 1 1 2— p-adic equations 13 3— The multiplicative group of Qp 15 Chapter III— Hubert symbol 19 1— Local properties 19 2— Global properties 23 Chapter ƒ K—Quadratic forms over Qp and over Q 27 1— Quadratic forms 27 2— Quadratic forms over Qp 35 3— Quadratic forms over Q 41 Appendix — Sums of three squares 45 Chapter V — Integral quadratic forms with discriminant ±1 48 1— Preliminaries 48 2— Statement of results 52 3— Proofs 55 Part II—Analytic Methods Chapter VI — The theorem on arithmetic progressions 61 1— Characters of finite abelian groups 61 2— Dirichlet series 64 3— Zeta function and L functions 68 4— Density and Dirichlet theorem 73 Chapter VII— Modular forms 77 1— The modular group 77 2— Modular functions 79 3— The space of modular forms g4 4— Expansions at infinity 90 5—Hecke operators 98 6— Theta functions 106 vii Bibliography 112 Index of Definitions 114 Index of Notations 115
adam_txt	Table of Contents Preface v Part I—Algebraic Methods Chapter /—Finite fields 3 1— Generalities 3 2— Equations over a finite field 5 3— Quadratic reciprocity law 6 Appendix — Another proof of the quadratic reciprocity law 9 Chapter Il—p-adk fields 1 j 1— The ring Zp and the field Qp 1 1 2— p-adic equations 13 3— The multiplicative group of Qp 15 Chapter III— Hubert symbol 19 1— Local properties 19 2— Global properties 23 Chapter ƒ K—Quadratic forms over Qp and over Q 27 1— Quadratic forms 27 2— Quadratic forms over Qp 35 3— Quadratic forms over Q 41 Appendix — Sums of three squares 45 Chapter V — Integral quadratic forms with discriminant ±1 48 1— Preliminaries 48 2— Statement of results 52 3— Proofs 55 Part II—Analytic Methods Chapter VI — The theorem on arithmetic progressions 61 1— Characters of finite abelian groups 61 2— Dirichlet series 64 3— Zeta function and L functions 68 4— Density and Dirichlet theorem 73 Chapter VII— Modular forms 77 1— The modular group 77 2— Modular functions 79 3— The space of modular forms g4 4— Expansions at infinity 90 5—Hecke operators 98 6— Theta functions 106 vii Bibliography 112 Index of Definitions 114 Index of Notations 115
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author	Serre, Jean-Pierre 1926-
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discipline	Mathematik
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edition	6. printing
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spelling	Serre, Jean-Pierre 1926- Verfasser (DE-588)142283126 aut Cours d'arithmétique A course in arithmetic J.-P. Serre 6. printing New York [u.a.] Springer [2001] VIII, 115 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 7 Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Analytische Zahlentheorie (DE-588)4001870-2 gnd rswk-swf Zahlkörper (DE-588)4067273-6 gnd rswk-swf Arithmetik (DE-588)4002919-0 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 s DE-604 Analytische Zahlentheorie (DE-588)4001870-2 s Zahlentheorie (DE-588)4067277-3 s Arithmetik (DE-588)4002919-0 s 1\p DE-604 Zahlkörper (DE-588)4067273-6 s 2\p DE-604 Graduate texts in mathematics 7 (DE-604)BV000000067 7 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014569795&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Serre, Jean-Pierre 1926- A course in arithmetic Graduate texts in mathematics Algebraische Zahlentheorie (DE-588)4001170-7 gnd Analytische Zahlentheorie (DE-588)4001870-2 gnd Zahlkörper (DE-588)4067273-6 gnd Arithmetik (DE-588)4002919-0 gnd Zahlentheorie (DE-588)4067277-3 gnd
subject_GND	(DE-588)4001170-7 (DE-588)4001870-2 (DE-588)4067273-6 (DE-588)4002919-0 (DE-588)4067277-3
title	A course in arithmetic
title_alt	Cours d'arithmétique
title_auth	A course in arithmetic
title_exact_search	A course in arithmetic
title_exact_search_txtP	A course in arithmetic
title_full	A course in arithmetic J.-P. Serre
title_fullStr	A course in arithmetic J.-P. Serre
title_full_unstemmed	A course in arithmetic J.-P. Serre
title_short	A course in arithmetic
title_sort	a course in arithmetic
topic	Algebraische Zahlentheorie (DE-588)4001170-7 gnd Analytische Zahlentheorie (DE-588)4001870-2 gnd Zahlkörper (DE-588)4067273-6 gnd Arithmetik (DE-588)4002919-0 gnd Zahlentheorie (DE-588)4067277-3 gnd
topic_facet	Algebraische Zahlentheorie Analytische Zahlentheorie Zahlkörper Arithmetik Zahlentheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014569795&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000067
work_keys_str_mv	AT serrejeanpierre coursdarithmetique AT serrejeanpierre acourseinarithmetic

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