Lectures on a method in the theory of exponential sums:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1987
|
| Series: | Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research lectures in mathematics and physics / Mathematics
80 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 134 S. |
| ISBN: | 3540183663 0387183663 |
Staff View
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| 245 | 1 | 0 | |a Lectures on a method in the theory of exponential sums |c by M. Jutila |
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Record in the Search Index
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| adam_text | CONTENTS
PREFACE
NOTATION
INTRODUCTION .. i
CHAPTER I. SUMMATION FORMULAE .. 8
§ 1.1 The function E(s,r) .. 9
§ 1.2 The function cp(s,r) .. 13
§ 1.3 Asymptotic formulae for the gamma function and
Bessel functions .. 17
§ 1.4 Evaluation of some complex integrals .. 20
§ 1.5 Approximate formulae and mean value estimates
for D(x,r) and A(x,r) .. 23
§ 1.6 Identities for D (x,r) and A (x,r) : the case
a . 1 ..33
§ 1.7 Analysis of the convergence of the Voronoi series.. 36
§ 1.8 Identities for D(x,r) and A(x,r) .. 40
§ 1.9 The summation formulae .. 43
NOTES .. 45
CHAPTER II. EXPONENTIAL INTEGRALS .. 49
§ 2.1 A saddle point theorem for smoothed exponential
integrals .. 49
§ 2.2 Smoothed exponential integrals without a saddle
point .. 63
NOTES .. 64
CHAPTER III. TRANSFORMATION FORMULAE FOR EXPONENTIAL SUMS .. 66
§ 3.1 Transformation of exponential sums .. 66
§ 3.2 Transformation of smoothed exponential sums .. 78
iii
CHAPTER IV. APPLICATIONS .. 85
§ 4.1 Transformation formulae for Dirichlet polynomials.. 85
§ 4.2 The order of cp( /2 + it) .. 93
§ 4.3 Estimation of long exponential sums .. 101
§ 4.4 The twelfth moment of t;(l/2 + it) and sixth
moment of cp( /2 + it) .. 112
NOTES .. 130
REFERENCES .. 132
|
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| id | DE-604.BV006560847 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:48:20Z |
| institution | BVB |
| isbn | 3540183663 0387183663 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004184262 |
| oclc_num | 17680954 |
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| physical | VIII, 134 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer |
| record_format | marc |
| series2 | Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research lectures in mathematics and physics / Mathematics |
| spelling | Jutila, Matti Verfasser aut Lectures on a method in the theory of exponential sums by M. Jutila Berlin [u.a.] Springer 1987 VIII, 134 S. txt rdacontent n rdamedia nc rdacarrier Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research lectures in mathematics and physics / Mathematics 80 Fonctions exponentielles ram Exponential functions Exponentialsumme (DE-588)4201355-0 gnd rswk-swf Exponentialsumme (DE-588)4201355-0 s DE-604 Mathematics Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research lectures in mathematics and physics 80 (DE-604)BV000015654 80 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004184262&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jutila, Matti Lectures on a method in the theory of exponential sums Fonctions exponentielles ram Exponential functions Exponentialsumme (DE-588)4201355-0 gnd |
| subject_GND | (DE-588)4201355-0 |
| title | Lectures on a method in the theory of exponential sums |
| title_auth | Lectures on a method in the theory of exponential sums |
| title_exact_search | Lectures on a method in the theory of exponential sums |
| title_full | Lectures on a method in the theory of exponential sums by M. Jutila |
| title_fullStr | Lectures on a method in the theory of exponential sums by M. Jutila |
| title_full_unstemmed | Lectures on a method in the theory of exponential sums by M. Jutila |
| title_short | Lectures on a method in the theory of exponential sums |
| title_sort | lectures on a method in the theory of exponential sums |
| topic | Fonctions exponentielles ram Exponential functions Exponentialsumme (DE-588)4201355-0 gnd |
| topic_facet | Fonctions exponentielles Exponential functions Exponentialsumme |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004184262&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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