Lectures on the Riemann zeta function:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2014]
|
| Series: | University lecture series
Volume 62 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | vii, 119 Seiten Diagramme |
| ISBN: | 9781470418519 |
Staff View
MARC
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| 245 | 1 | 0 | |a Lectures on the Riemann zeta function |c H. Iwaniec |
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| 264 | 4 | |c © 2014 | |
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Record in the Search Index
| _version_ | 1804152428424069120 |
|---|---|
| adam_text | Contents
Preface
vii
Part
1.
Classical Topics
1
Chapter I- Panorama of Arithmetic Functions
3
Chapter
2.
The
Euler-
МаЫашт
Formula
9
Chapter
3.
Tchebyshmrts Prime Seeds
13
Chapter
1.
Elementary Prime Number Theorem
15
Chapter
5.
The
Шешаїш
Memoir
21
Chapter
6.
The Analytic Continuation
23
Chapter
7.
The Functional Equation
25
Chapter
8.
The Product Formula over the Zeros
27
Chapter
9.
The Asymptotic Formula for N{T)
33
Chapter
10.
Тіш
Asymptotic Formula for
Фїяп
37
Chapter
11.
The Zero-free Region
atui
the PNT
41
Chapter
12.
Approximate Functional Equations
43
Chapter
13.
The Dirklilet Polynomials
47
Chapter
14.
Zeros off the Critical Line
55
Chapter
15*
Zeros on tlte Critical Line
57
Part
2.
The Critical Zeros after Levmson
63
Chapter
16.
Introduction
Ш
Chaptrer
17.
Detecting Critical
Zcïos
67
Chapter IS.
Соигеу й
Construction
69
CiiaptiPr W.
Тће
Ащишеш
Variations
71
2Ö.
Attaeîiing
a
^lolSifier
7б
The Riemann
zeta
function was introduced by
L
Euler
(1737)
in connection with ques¬
tions about the distribution of prime numbers. Later, B. Riemann
(1859)
derived deeper
results about the prime numbers by considering the
zeta
function in the complex variable.
The famous Riemann Hypothesis, asserting that all of the non-trivial zeros of
zeta are
on
a critical line in the complex plane, is one of the most important unsolved problems in
modern mathematics.
The present book consists of two pans. The first part covers classical material about the
/eros
of the Riemann
/eia
function with applications to the distribution of prime numbers,
including those made by Riemann himself,
К
Carlson, and Hardy-Littlewood. The second
pan gives a complete presentation of Levinson s method for zeros on the critical line,
which allows one to prove, in particular, that more than one-third of non-trivial zeros
of
/eia are
on the critical line. This approach and some results concerning integrals of
Dirichlet polynomials are new. There are also technical lemmas which can be useful in a
broader context.
The Riemann
zeta
function was introduced by
L
Euler
(1737)
in connection with ques¬
tions about the distribution of prime numbers. Later, B. Riemann
(1859)
derived deeper
results about the prime numbers by considering the
zeta
function in the complex variable.
The famous Riemann Hypothesis, asserting that all of the non-trivial zeros of
zeta are
on
a critical line in the complex plane, is one of the most important unsolved problems in
modern mathematics.
The present book consists of two parts. The first part covers classical material about the
/cros
of the Riemann
zeta
function with applications to the distribution of prime numbers,
including those made by Riemann himself,
E
Carlson, and Hardy-Littlewood, The second
part gives a complete presentation of Levinson s method for zeros on the critical line,
which allows one to prove, in particular, that more than one-third of non-trivial zeros
of /eta are on the critical line. This approach and some results concerning integrals of
Dirichlet polynomials are new. There are also technical lemmas which can be useful in a
broader context,
|
| any_adam_object | 1 |
| author | Iwaniec, Henryk 1947- |
| author_GND | (DE-588)141817569 |
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| bvnumber | BV042014357 |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042014357 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:10:33Z |
| institution | BVB |
| isbn | 9781470418519 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027456183 |
| oclc_num | 897358586 |
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| physical | vii, 119 Seiten Diagramme |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Iwaniec, Henryk 1947- Verfasser (DE-588)141817569 aut Lectures on the Riemann zeta function H. Iwaniec Providence, Rhode Island American Mathematical Society [2014] © 2014 vii, 119 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 62 Riemannsche Zetafunktion (DE-588)4308419-9 gnd rswk-swf Riemannsche Zetafunktion (DE-588)4308419-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1891-5 University lecture series Volume 62 (DE-604)BV004153846 62 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027456183&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027456183&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Iwaniec, Henryk 1947- Lectures on the Riemann zeta function University lecture series Riemannsche Zetafunktion (DE-588)4308419-9 gnd |
| subject_GND | (DE-588)4308419-9 |
| title | Lectures on the Riemann zeta function |
| title_auth | Lectures on the Riemann zeta function |
| title_exact_search | Lectures on the Riemann zeta function |
| title_full | Lectures on the Riemann zeta function H. Iwaniec |
| title_fullStr | Lectures on the Riemann zeta function H. Iwaniec |
| title_full_unstemmed | Lectures on the Riemann zeta function H. Iwaniec |
| title_short | Lectures on the Riemann zeta function |
| title_sort | lectures on the riemann zeta function |
| topic | Riemannsche Zetafunktion (DE-588)4308419-9 gnd |
| topic_facet | Riemannsche Zetafunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027456183&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027456183&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
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