Multiplicative number theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Edition: | 3. ed. |
| Series: | Graduate texts in mathematics
74 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 177 S. |
| ISBN: | 0387950974 |
Staff View
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Record in the Search Index
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| adam_text | CONTENTS
Preface to the Second and Third Editions
vii
Preface to the First Edition
ix
Bibliography
xi
Notation
xiii
1
Primes in Arithmetic Progression
1
2
Gauss Sum
12
3
Cyclotomy
17
4
Primes in Arithmetic Progression
:
The General
Modulus
27
5
Primitive Characters
35
6
Dirichlet s Class Number Formula
43
7
The Distribution of the Primes
54
8
Riemann s Memoir
59
9
The Functional Equation of the
L
Functions
65
10
Properties of the
Γ
Function
73
11
Integral Functions of Order
1
74
12
The Infinite Products for ¿(s) and ¿(s,
χ)
79
13
A Zero-Free Region for £(s)
84
14
Zero-Free Regions for
Цѕ,
χ)
88
15
The Number N(T)
97
16
The Number N(T,
χ)
101
17
The Explicit Formula for
ψ(χ)
104
18
The Prime Number Theorem
111
19
The Explicit Formula for
ψ(χ, χ)
115
20
The Prime Number Theorem for Arithmetic
Progressions
([)
121
21
Siegel s Theorem
126
22
The Prime Number Theorem for Arithmetic
Progressions
(ID
132
23
The
Pólya-
Vinogradov Inequality
135
24
Further Prime Number Sums
138
25
An Exponential Sum Formed with Primes
143
26
Sums of Three Primes
145
27
The Large Sieve
151
28
Bombieri s Theorem
161
29
An Average Result
169
ЗО
References to Other Work
172
Index
175
|
| adam_txt |
CONTENTS
Preface to the Second and Third Editions
vii
Preface to the First Edition
ix
Bibliography
xi
Notation
xiii
1
Primes in Arithmetic Progression
1
2
Gauss' Sum
12
3
Cyclotomy
17
4
Primes in Arithmetic Progression
:
The General
Modulus
27
5
Primitive Characters
35
6
Dirichlet's Class Number Formula
43
7
The Distribution of the Primes
54
8
Riemann's Memoir
59
9
The Functional Equation of the
L
Functions
65
10
Properties of the
Γ
Function
73
11
Integral Functions of Order
1
74
12
The Infinite Products for ¿(s) and ¿(s,
χ)
79
13
A Zero-Free Region for £(s)
84
14
Zero-Free Regions for
Цѕ,
χ)
88
15
The Number N(T)
97
16
The Number N(T,
χ)
101
17
The Explicit Formula for
ψ(χ)
104
18
The Prime Number Theorem
111
19
The Explicit Formula for
ψ(χ, χ)
115
20
The Prime Number Theorem for Arithmetic
Progressions
([)
121
21
Siegel's Theorem
126
22
The Prime Number Theorem for Arithmetic
Progressions
(ID
132
23
The
Pólya-
Vinogradov Inequality
135
24
Further Prime Number Sums
138
25
An Exponential Sum Formed with Primes
143
26
Sums of Three Primes
145
27
The Large Sieve
151
28
Bombieri's Theorem
161
29
An Average Result
169
ЗО
References to Other Work
172
Index
175 |
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| edition | 3. ed. |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T14:58:39Z |
| indexdate | 2024-07-09T20:40:27Z |
| institution | BVB |
| isbn | 0387950974 |
| language | English |
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| physical | XIII, 177 S. |
| publishDate | 2000 |
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| publisher | Springer |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Davenport, Harold Verfasser aut Multiplicative number theory Harold Davenport 3. ed. rev. by Hugh L. Montgomery New York [u.a.] Springer 2000 XIII, 177 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 74 Multiplikative Zahlentheorie Number theory Numbers, Prime Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Primzahl (DE-588)4047263-2 gnd rswk-swf Multiplikative Zahlentheorie (DE-588)4040699-4 gnd rswk-swf Primzahl (DE-588)4047263-2 s DE-604 Multiplikative Zahlentheorie (DE-588)4040699-4 s Zahlentheorie (DE-588)4067277-3 s Montgomery, Hugh L. 1944- Sonstige (DE-588)172262968 oth Graduate texts in mathematics 74 (DE-604)BV000000067 74 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014850474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Davenport, Harold Multiplicative number theory Graduate texts in mathematics Multiplikative Zahlentheorie Number theory Numbers, Prime Zahlentheorie (DE-588)4067277-3 gnd Primzahl (DE-588)4047263-2 gnd Multiplikative Zahlentheorie (DE-588)4040699-4 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4047263-2 (DE-588)4040699-4 |
| title | Multiplicative number theory |
| title_auth | Multiplicative number theory |
| title_exact_search | Multiplicative number theory |
| title_exact_search_txtP | Multiplicative number theory |
| title_full | Multiplicative number theory Harold Davenport |
| title_fullStr | Multiplicative number theory Harold Davenport |
| title_full_unstemmed | Multiplicative number theory Harold Davenport |
| title_short | Multiplicative number theory |
| title_sort | multiplicative number theory |
| topic | Multiplikative Zahlentheorie Number theory Numbers, Prime Zahlentheorie (DE-588)4067277-3 gnd Primzahl (DE-588)4047263-2 gnd Multiplikative Zahlentheorie (DE-588)4040699-4 gnd |
| topic_facet | Multiplikative Zahlentheorie Number theory Numbers, Prime Zahlentheorie Primzahl |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014850474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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