Lectures on mean values of the Riemann zeta function:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin <<[u.a.]>>
Springer
1991
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| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018359652&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | V, 363 S. |
| ISBN: | 3540547487 0387547487 |
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Record in the Search Index
| _version_ | 1819348684017500160 |
|---|---|
| adam_text | CONTENTS
PREFACE
NOTATION
CHAPTER I. ELEMENTARY THEORY
§1.1 Basic properties of C(s) 1
§1.2 Elementary mean value theorems 4
§1.3 Bounds over short intervals 9
§1.4 Lower bounds for mean values over
short intervals 15
NOTES 19
CHAPTER II. THE ERROR TERMS IN MEAN SQUARE FORMULAS
§2.1 The mean square formulas 27
§2.2 The beginning of proof 30
§2.3 Transformation of the expressions
for the error terms 35
§2.4 Evaluation of some exponential integrals 46
§2.5 Completion of the proof of the mean
square formulas 50
§2.6 The mean square formula for E(T) 58
§2.7 The upper bounds for the error terms 74
§2.8 Asymptotic mean square of the product
of the zeta-function and a Dirichlet
polynomial 91
NOTES 95
CHAPTER III. THE INTEGRALS OF THE ERROR TERMS IN
MEAN SQUARE FORMULAS
§3.1 The formulas for the integrated
error terms 101
§3-2 The omega-results 121
§3-3 The mean square formulas 142
§3.4 The zeros of E(T) - % 146
§3«5 Some other results 152
NOTES 161
CHAPTER IV. A GENERAL STUDY OF EVEN MOMENTS
§4.1 The error term for the 2k-th moment 165
§4.2 The approximate functional equation 171
§4.3 Evaluation of Ik(T) 180
§4.4 Evaluation of the first main term 189
§4.5 The mean square formula 196
§4.6 The fourth power moment 203
§4.7 The sixth power moment 214
NOTES 219
CHAPTER V. MOTOHASHI S FORMULA FOR THE FOURTH MOMENT
§5-1 Introduction and statement of results 224
§5-2 Analytic continuation 231
§5-3 Application of spectral theory and
Kuznetsov s trace formula 240
§5«4 Further analytic continuation and the
explicit formula 254
§5-5 Deductions from the explicit formula 263
§5«6 Upper bounds 282
§5.7 The omega-result 295
NOTES 311
CHAPTER VI. FRACTIONAL MEAN VALUES
§6.1 Upper and lower bounds for fractional
mean values 317
§6.2 An asymptotic formula for mean values 330
§6.3 The value distribution on the critical
line 334
§6.4 Mean values over short intervals 339
NOTES 347
REFERENCES 350
|
| any_adam_object | 1 |
| author | Ivić, Aleksandar 1949-2020 |
| author_GND | (DE-588)1037259343 |
| author_facet | Ivić, Aleksandar 1949-2020 |
| author_role | aut |
| author_sort | Ivić, Aleksandar 1949-2020 |
| author_variant | a i ai |
| building | Verbundindex |
| bvnumber | BV024379744 |
| classification_rvk | SI 890 SK 680 |
| ctrlnum | (OCoLC)263273488 (DE-599)BVBBV024379744 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV024379744 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:54:13Z |
| institution | BVB |
| isbn | 3540547487 0387547487 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018359652 |
| oclc_num | 263273488 |
| open_access_boolean | |
| owner | DE-83 DE-188 |
| owner_facet | DE-83 DE-188 |
| physical | V, 363 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Ivić, Aleksandar 1949-2020 Lectures on mean values of the Riemann zeta function Mittelwert (DE-588)4130070-1 gnd Riemannsche Zetafunktion (DE-588)4308419-9 gnd |
| subject_GND | (DE-588)4130070-1 (DE-588)4308419-9 |
| title | Lectures on mean values of the Riemann zeta function |
| title_auth | Lectures on mean values of the Riemann zeta function |
| title_exact_search | Lectures on mean values of the Riemann zeta function |
| title_full | Lectures on mean values of the Riemann zeta function by A. Ivic |
| title_fullStr | Lectures on mean values of the Riemann zeta function by A. Ivic |
| title_full_unstemmed | Lectures on mean values of the Riemann zeta function by A. Ivic |
| title_short | Lectures on mean values of the Riemann zeta function |
| title_sort | lectures on mean values of the riemann zeta function |
| topic | Mittelwert (DE-588)4130070-1 gnd Riemannsche Zetafunktion (DE-588)4308419-9 gnd |
| topic_facet | Mittelwert Riemannsche Zetafunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018359652&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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