Not always buried deep: a second course in elementary number theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2009]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xv, 303 Seiten Illustrationen, Diagramme |
| ISBN: | 9780821848807 |
Internformat
MARC
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| 245 | 1 | 0 | |a Not always buried deep |b a second course in elementary number theory |c Paul Pollack |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2009] | |
| 264 | 4 | |c © 2009 | |
| 300 | |a xv, 303 Seiten |b Illustrationen, Diagramme | ||
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| 338 | |b nc |2 rdacarrier | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017737030 | ||
Datensatz im Suchindex
| _version_ | 1804139390304256000 |
|---|---|
| adam_text | Contents
Foreword
Xi
Notation xiii
Acknowledgements
xiv
Chapter
1.
Elementary Prime Number Theory, I I
§1.
Introduction I
§2.
Euclid and his imitators
%
§3.
Coprirne
integer sequences
ă
§4.
The Euler-Riemann
zeta
function
4
§5.
Squarefree and smooth numbers
9
§6.
Sledgehammers!
12
§7.
Prime-producing formulas
13
§8.
Euler s prime-producing polynomial
14
§9.
Primes represented by general polynomials
22
§10.
Primes and composites in other sequences
29
Notes
32
Exercises
34
Chapter
2.
Cyclotomy
45
§1.
Introduction
45
§2.
An algebraic criterion for constructibility
50
§3.
Much ado about
Ζ[ζρ]
52
§4.
Completion of the proof of the Gauss-Wantzel theorem
55
§5.
Period polynomials and Kummer s criterion
57
vii
VUl
Contents
§6.
A cyclotomic proof of quadratic reciprocity
61
§7.
Jacobi s cubic reciprocity law
64
Notes
75
Exercises
77
Chapter
3.
Elementary Prime Number Theory, II
85
§1.
Introduction
85
§2.
The set of prime numbers has density zero
88
§3.
Three theorems of Chebyshev
89
§4.
The work of Mertens
95
§5.
Primes and probability
100
Notes
104
Exercises
107
Chapter
4.
Primes in Arithmetic Progressions
119
§1.
Introduction
119
§2.
Progressions modulo
4 120
§3.
The characters of a finite abelian group
123
§4.
The L-series at
s
= 1 127
§5.
Nonvanishing of L(l,x) for complex
χ
128
§6.
Nonvanishing of L(l,
χ)
for real
χ
132
§7.
Finishing up
133
§8.
Sums of three squares
134
Notes
139
Exercises
141
Chapter
5.
Interlude: A Proof of the Hubert-Waring Theorem
151
§1.
Introduction
151
§2.
Proof of the Hubert-Waring theorem (Theorem
5.1) 152
§3.
Producing the Hilbert-Dress identities
156
Notes
161
Chapter
6.
Sieve Methods
163
§1.
Introduction
163
§2.
The general sieve problem: Notation and preliminaries
169
§3.
The sieve of Eratosthenes-Legendre and its applications
170
§4.
Brun s pure sieve
175
§5.
The Brun-Hooley sieve
182
Contents ix
§6. An
application
to the
Goldbach
problem
196
Notes
201
Exercises
202
Chapter
7.
An Elementary Proof of the Prime Number Theorem
213
§1.
Introduction
214
§2.
Chebyshev s theorems revisited
217
§3.
Proof of Selberg s fundamental formula
221
§4.
Removing the explicit appearance of primes
224
§5.
Nevanlinna s finishing strategy
231
Notes
235
Exercises
237
Chapter
8.
Perfect Numbers and their Friends
247
§1.
Introduction and overview
248
§2.
Proof of
Dickson s fmiteness
theorem
253
§3.
How rare are odd perfect numbers?
255
§4.
The distribution function of
σ(η)/η
259
§5.
Sociable numbers
263
Notes
267
Exercises
269
References
279
Index
301
|
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| id | DE-604.BV035682785 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:43:19Z |
| institution | BVB |
| isbn | 9780821848807 |
| language | English |
| lccn | 2009023766 |
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| physical | xv, 303 Seiten Illustrationen, Diagramme |
| publishDate | 2009 |
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| publisher | American Mathematical Society |
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| spelling | Pollack, Paul 1980- Verfasser (DE-588)143962892 aut Not always buried deep a second course in elementary number theory Paul Pollack Providence, Rhode Island American Mathematical Society [2009] © 2009 xv, 303 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1207-4 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017737030&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pollack, Paul 1980- Not always buried deep a second course in elementary number theory Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | Not always buried deep a second course in elementary number theory |
| title_auth | Not always buried deep a second course in elementary number theory |
| title_exact_search | Not always buried deep a second course in elementary number theory |
| title_full | Not always buried deep a second course in elementary number theory Paul Pollack |
| title_fullStr | Not always buried deep a second course in elementary number theory Paul Pollack |
| title_full_unstemmed | Not always buried deep a second course in elementary number theory Paul Pollack |
| title_short | Not always buried deep |
| title_sort | not always buried deep a second course in elementary number theory |
| title_sub | a second course in elementary number theory |
| topic | Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Number theory Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017737030&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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