Analytic number theory for undergraduates:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2009
|
| Series: | Monographs in number theory
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 113 S. |
| ISBN: | 9789814271363 9814271365 9789814271356 9814271357 |
Staff View
MARC
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| 245 | 1 | 0 | |a Analytic number theory for undergraduates |c Heng Huat Chan |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2009 | |
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Record in the Search Index
| _version_ | 1804139174206373889 |
|---|---|
| adam_text | Contents
Preface
vii
1.
The
Fundamental
Theorem
of Arithmetic
1
1.1
Least Integer Axiom and Mathematical Induction
..... 1
1.2
Division Algorithm
...................... 2
1.3
Greatest common divisors
.................. 4
1.4
The Euclidean Algorithm
.................. 7
1.5
Congruences
.......................... 8
1.6
Fundamental Theorem of Arithmetic
............ 10
1.7
Exercises
........................... 11
2.
Arithmetical Functions and Dirichlet Multiplication
13
2.1
The
Möbius
function
..................... 13
2.2
The
Euler totient
function
.................. 15
2.3
Dirichlet product
....................... 20
2.4
Dirichlet inverses and the
Möbius
inversion formula
.... 22
2.5
Multiplicative functions and Dirichlet products
...... 23
2.6
Exercises
........................... 25
3.
Averages of Arithmetical Functions
29
3.1
Introduction
.......................... 29
3.2
Partial summation and the Euler-Maclaurin summation
formula
............................ 30
3.3
Some elementary asymptotic formulas
........... 33
3.4
The divisor function and
Dírichleťs
hyperbola method
. . 35
3.5
An application of the hyperbola method
.......... 37
x
Analytic Number Theory for Undergraduates
3.6
Exercises
........................... 39
4.
Elementary Results on the Distribution of Primes
41
4.1
Introduction
.......................... 41
4.2
The function
ψ(χ)
...................... 42
4.3
The functions
θ(χ)
and
π
(ж).................
44
4.4
Merten s estimates
...................... 46
4.5
Prime Number Theorem and
Μ (μ).............
49
4.6
The
Bertrand
Postulate
................... 54
4.7
Exercises
........................... 59
5.
The Prime Number Theorem
63
5.1
The Prime Number Theorem
................ 63
5.2
The Riemann
zeta
function
................. 63
5.3
Euler s product and the product representation of C(s)
. . 64
5.4
Analytic continuation of £(s) to
σ
> 0........... 67
5.5
Upper bounds for
ζ(β)
and
( {s)
near
σ
= 1....... 68
5.6
The non-vanishing of
ζ(1
+ it)
................ 70
5.7
A lower bound for |C(s)| near
σ
= 1 ............ 73
5.8
Perron s Formula
....................... 76
5.9
Completion of the proof of the Prime Number Theorem
. 80
5.10
Exercises
........................... 84
6.
Dirichlet Series
85
6.1
Absolute convergence of a Dirichlet series
......... 85
6.2
The Uniqueness Theorem
.................. 86
6.3
Multiplication of Dirichlet series
.............. 87
6.4
Conditional convergence of Dirichlet series
......... 88
6.5
Landau s Theorem for Dirichlet series
........... 91
6.6
Exercises
........................... 92
7.
Primes in Arithmetic Progression
95
7.1
Introduction
.......................... 95
7.2
Dirichlet s characters
..................... 96
7.3
The orthogonal relations
................... 98
7.4
The Dirichlet L-series
.................... 100
7.5
Proof of Dirichlet s Theorem
................ 101
7.6
Exercises
........................... 106
Contents xl
109
Bibliography
111
Notation
113
Index
|
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV035536324 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:39:53Z |
| institution | BVB |
| isbn | 9789814271363 9814271365 9789814271356 9814271357 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017592448 |
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| physical | XI, 113 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific |
| record_format | marc |
| series | Monographs in number theory |
| series2 | Monographs in number theory |
| spelling | Chan, Heng Huat Verfasser aut Analytic number theory for undergraduates Heng Huat Chan Singapore [u.a.] World Scientific 2009 XI, 113 S. txt rdacontent n rdamedia nc rdacarrier Monographs in number theory 3 Number theory Analytische Zahlentheorie (DE-588)4001870-2 gnd rswk-swf Analytische Zahlentheorie (DE-588)4001870-2 s DE-604 Monographs in number theory 3 (DE-604)BV035341434 3 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017592448&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chan, Heng Huat Analytic number theory for undergraduates Monographs in number theory Number theory Analytische Zahlentheorie (DE-588)4001870-2 gnd |
| subject_GND | (DE-588)4001870-2 |
| title | Analytic number theory for undergraduates |
| title_auth | Analytic number theory for undergraduates |
| title_exact_search | Analytic number theory for undergraduates |
| title_full | Analytic number theory for undergraduates Heng Huat Chan |
| title_fullStr | Analytic number theory for undergraduates Heng Huat Chan |
| title_full_unstemmed | Analytic number theory for undergraduates Heng Huat Chan |
| title_short | Analytic number theory for undergraduates |
| title_sort | analytic number theory for undergraduates |
| topic | Number theory Analytische Zahlentheorie (DE-588)4001870-2 gnd |
| topic_facet | Number theory Analytische Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017592448&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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