Zeta functions over zeros of zeta functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Schriftenreihe: | Lecture notes of the Unione Matematica Italiana
8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XVI, 163 S. graph. Darst. |
| ISBN: | 9783642052026 |
Internformat
MARC
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| 245 | 1 | 0 | |a Zeta functions over zeros of zeta functions |c André Voros |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XVI, 163 S. |b graph. Darst. | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020190808 | ||
Datensatz im Suchindex
| _version_ | 1804142776954126337 |
|---|---|
| adam_text | 28 CONTENTS PREFACE VII LIST OF SPECIAL SYMBOLS XV 1 INTRODUCTION 1 1.1
SYMMETRIC FUNCTIONS 1 1.2 ESSENTIAL BASIC NOTATION 3 1.3 THE POISSON
SUMMATION FORMULA 4 1.4 EULER-MACLAURIN SUMMATION FORMULAE 5 1.5
MEROMORPHIC PROPERTIES OF MELLIN TRANSFORMS 6 2 INFINITE PRODUCTS AND
ZETA-REGULARIZATION 9 2.1 INFORMAL DISCUSSION 9 2.2 A CLASS OF ELIGIBLE
SEQUENCES {X K } 12 2.3 MEROMORPHIC CONTINUATION OF THE ZETA FUNCTION 12
2.4 THE GENERALIZED ZETA FUNCTION 14 2.5 THE ZETA-REGULARIZED PRODUCT 15
2.C PRACTICAL RESULTS 18 2.6.1 ZETA-REGULARIZATION: A ZETA-FREE RECIPE
18 2.6.2 A SUBCLASS: THETA-ELIGIBLE SEQUENCES 19 2.G.3 EXPLICIT
PROPERTIES OF THE GENERALIZED ZETA FUNCTION. 21 3 THE RIEMANN ZETA
FUNCTION C(X): * PRIMER 23 3.1 DEFINITION AND IMMEDIATE PROPERTIES 23
3.2 THE EULER INFINITE PRODUCT 24 3.3 THE STIELTJES AND CUMULANT
EXPANSIONS 24 3.4 THE FUNCTIONAL EQUATION AND COMPLETED ZETA FUNCTION
EL(X) 25 3.5 THE DIRICHLET BETA FUNCTION 0{X) 28 3.6 THE HURWITZ ZETA
FUNCTION C,(X,W) BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/997433078 DIGITALISIERT DURCH CONTENTS RIEMANN ZEROS
AND FACTORIZATIONS OF THE ZETA FUNCTION 33 4.1 GROWTH PROPERTIES OF C(X)
AND E(X) 33 4.2 THE RIEMANN ZEROS (BASIC FEATURES) 34 4.3 HADAMARD
PRODUCTS FOR S(X) 35 4.4 BASIC BOUNDS ON C /C 36 4.5 THE (ASYMPTOTIC)
RIEMANN-VON MANGOLDT FORMULA 39 SUPERZETA FUNCTIONS: AN OVERVIEW 41 5.1
FIRST KIND ($R) 42 5.2 SECOND KIND (Z) 42 5.3 THIRD KIND (3) 44 5.4
FURTHER GENERALIZATIONS (LERCH, CRAMER, ... ) 44 5.5 OTHER STUDIES ON
SUPERZETA FUNCTIONS 45 EXPLICIT FORMULAE 49 6.1 THE GUINAND-WEIL
EXPLICIT FORMULA 49 6.2 DERIVATION OF THE EXPLICIT FORMULA 50 6.3
PATTERN-MATCHING WITH THE SELBERG TRACE FORMULA 52 6.3.1 THE SELBERG
TRACE FORMULA (COMPACT SURFACE CASE) 52 6.3.2 COMPARISON WITH THE
EXPLICIT FORMULA 53 6.4 EXPLICIT FORMULAE FOR THE SUPERZETA FUNCTIONS 54
6.4.1 THE FAMILY OF THE FIRST KIND 2* 54 6.4.2 THE FAMILY OF THE SECOND
KIND Z 56 6.4.3 CONCLUDING REMARKS 58 THE FAMILY OF THE FIRST KIND {2?{S
T)} 59 7.1 THE BASIC ANALYTICAL CONTINUATION FORMULA 59 7.2 DERIVATIONS
60 7.2. CONTENTS XIII 8 THE FAMILY OF THE SECOND KIND {Z(CR 1 1)} 75 8.1
THE CONFLUENT CASE Z{O T = 0) = ZO(O) 76 8.2 MEROMORPHIC CONTINUATION
IN A FOR GENERAL T 77 8.3 ALGEBRAIC RESULTS FOR Z(A T) AT GENERAL T 79
8.4 TRANSCENDENTAL VALUES OF Z{O T) FOR GENERALI 80 8.5 IMPRINTS OF
THE CENTRAL SYMMETRY P * (1 * P) 80 8.6 RESULTS FOR Z(A T) AT T = 0
AND T = 82 8.6.1 THE FUNCTION .20 (S) (THE CONFLUENT CASE T = 0) 82
8.6.2 THE FUNCTION Z*(S) (THE CASE T = ) 82 8.7 TABLES OF FORMULAE FOR
THE SPECIAL VALUES OF Z 84 8.7.1 FUNCTION OF SECOND KIND FOR GENERAL I
84 8.7.2 FUNCTION OF SECOND KIND AT T = 0 AND XIV CONTENTS 11.2.1 THE
CASE [RH FALSE] 116 11.2.2 THE CASE [RH TRUE] 117 11.2.3 RECAPITULATION
AND DISCUSSION 118 11.3 AN EVEN MORE SENSITIVE SEQUENCE 119 11.4 MORE
GENERAL CASES: A SUMMARY 121 A NUMERICAL EXPLORATIONS 123 A.I SUPERZETA
FUNCTIONS OF THE SECOND KIND 123 A.2 SUPERZETA FUNCTIONS OF THE FIRST
KIND 125 A.3 NUMERICAL TABLES 126 * THE SELBERG CASE 129 B.I SUPERZETA
FUNCTIONS OF THE FIRST KIND 130 B.2 SUPERZETA FUNCTIONS OF THE SECOND
KIND 132 B.3 TABLES OF SPECIAL-VALUE FORMULAE (SELBERG CASES) 134 C ON
THE LOGARITHMIC DERIVATIVES AT I 137 D ON THE ZEROS OF THE ZETA FUNCTION
BY HJ. MELLIN (1917) 139 REFERENCES 153 INDEX 159
|
| any_adam_object | 1 |
| author | Voros, André |
| author_facet | Voros, André |
| author_role | aut |
| author_sort | Voros, André |
| author_variant | a v av |
| building | Verbundindex |
| bvnumber | BV025594720 |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)502403387 (DE-599)BVBBV025594720 |
| dewey-full | 512.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.73 |
| dewey-search | 512.73 |
| dewey-sort | 3512.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV025594720 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:37:09Z |
| institution | BVB |
| isbn | 9783642052026 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020190808 |
| oclc_num | 502403387 |
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| owner | DE-11 DE-19 DE-BY-UBM DE-824 DE-20 |
| owner_facet | DE-11 DE-19 DE-BY-UBM DE-824 DE-20 |
| physical | XVI, 163 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series2 | Lecture notes of the Unione Matematica Italiana |
| spelling | Voros, André Verfasser aut Zeta functions over zeros of zeta functions André Voros Berlin [u.a.] Springer 2010 XVI, 163 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes of the Unione Matematica Italiana 8 Literaturangaben Zetafunktion (DE-588)4190764-4 gnd rswk-swf Zetafunktion (DE-588)4190764-4 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-05203-3 Unione Matematica Italiana Lecture notes of the Unione Matematica Italiana 8 (DE-604)BV022297190 8 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020190808&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Voros, André Zeta functions over zeros of zeta functions Zetafunktion (DE-588)4190764-4 gnd |
| subject_GND | (DE-588)4190764-4 |
| title | Zeta functions over zeros of zeta functions |
| title_auth | Zeta functions over zeros of zeta functions |
| title_exact_search | Zeta functions over zeros of zeta functions |
| title_full | Zeta functions over zeros of zeta functions André Voros |
| title_fullStr | Zeta functions over zeros of zeta functions André Voros |
| title_full_unstemmed | Zeta functions over zeros of zeta functions André Voros |
| title_short | Zeta functions over zeros of zeta functions |
| title_sort | zeta functions over zeros of zeta functions |
| topic | Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Zetafunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020190808&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022297190 |
| work_keys_str_mv | AT vorosandre zetafunctionsoverzerosofzetafunctions |