Multiple trigonometric sums:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence ; Rhode Island
American Mathematical Society
1982
|
| Series: | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics
151 = 1982,2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russischen übersetzt |
| Physical Description: | viii, 126 Seiten |
| ISBN: | 0821830678 |
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Record in the Search Index
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|---|---|
| adam_text | PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
IN THE ACADEMY OF SCIENCES OF THE USSR
TABLE OF CONTENTS
Basic Notation 1
Introduction 3
CHAPTER I. Theorem on the mean value 11
§ 1. One dimensional theorem on the mean value of a power of the modulus
of a trigonometric sum (estimate for Vinogradov s integral) 11
1. Lemma on prime numbers in intervals 12
2. Lemma on the number of solutions of a complete system of congruences 15
3. The basic recurrence inequality 16
4. The general theorem 19
5. Estimate for Vinogradov s integral for k small relative to n2 21
6. Estimate for Vinogradov s integral for k large relative to ri1 22
7. Concerning p adic methods for proving Vinogradov s theorem on the
mean value 23
§2. Theorem on the mean value of a power of the modulus of a multiple
trigonometric sum 27
1. Definitions 29
2. Some simple lemmas 29
3. Lemma on the number of solutions of a complete system of congruences 30
4. The fundamental lemma 36
5. The theorem on the mean value 43
CHAPTER II. Estimates for multiple trigonometric sums 47
§ 1. Multiple trigonometric integrals and complete multiple rational trigono¬
metric sums 47
1. Lemmas on multiple trigonometric integrals 47
2. Lemmas on complete multiple rational trigonometric sums 52
§2. Estimates for multiple trigonometric sums which depend on the properties
of one of the coefficients of the polynomial in the exponent (simplest esti¬
mates) 55
1. Auxiliary lemmas 55
2. The theorem 56
§3. General estimate for a multiple trigonometric sum 58
1. Lemmas on the multiplicity of intersection of the regions 59
2. Generalization of van der Korput s lemma 69
3. The general estimate 70
§4. Estimate for a complete rational multiple trigonometric sum from the
theorem on the mean value 80
v
CHAPTER III. Applications of the theory of multiple trigonometric sums 85
§ 1. A sharp upper bound for the number of solutions of complete and in¬
complete systems of equations 85
1 . Statement of the problem 85
2. The theorems 86
3. Estimates from below 93
§2. Asymptotic formulas for the number of solutions of complete and incom¬
plete systems of equations 94
1. Statement of the problem 94
2. Asymptotic formulas 95
§3. Distribution of the fractional parts of polynomials in several variables 117
1. Joint distribution 117
2. Distribution of fractional parts in multidimensional regions 120
Conclusion. Possible generalizations and problems 123
Bibliography 125
vi
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| any_adam_object | 1 |
| author | Archipov, Gennadij I. 1945- Karacuba, Anatolij Alekseevič 1937-2008 Čubarikov, Vladimir Nikolaevič |
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| author_facet | Archipov, Gennadij I. 1945- Karacuba, Anatolij Alekseevič 1937-2008 Čubarikov, Vladimir Nikolaevič |
| author_role | aut aut aut |
| author_sort | Archipov, Gennadij I. 1945- |
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| building | Verbundindex |
| bvnumber | BV000246206 |
| classification_rvk | SI 700 |
| ctrlnum | (OCoLC)260150990 (DE-599)BVBBV000246206 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000246206 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:11:02Z |
| institution | BVB |
| isbn | 0821830678 |
| language | English |
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| physical | viii, 126 Seiten |
| publishDate | 1982 |
| publishDateSearch | 1982 |
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| publisher | American Mathematical Society |
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| series | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |
| series2 | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |
| spelling | Archipov, Gennadij I. 1945- (DE-588)129604909 aut Kratnye trigonometričeskie summy Multiple trigonometric sums by G. I. Arhipov ; A. A. Karacuba and V. N. Čubarikov Providence ; Rhode Island American Mathematical Society 1982 viii, 126 Seiten txt rdacontent n rdamedia nc rdacarrier Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics 151 = 1982,2 Aus dem Russischen übersetzt Trigonometrisches Polynom (DE-588)4806392-7 gnd rswk-swf Trigonometrisches Polynom (DE-588)4806392-7 s DE-604 Karacuba, Anatolij Alekseevič 1937-2008 (DE-588)1024789535 aut Čubarikov, Vladimir Nikolaevič (DE-588)1067790128 aut Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics 151 = 1982,2 (DE-604)BV000009943 151 = 1982,2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000148148&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Archipov, Gennadij I. 1945- Karacuba, Anatolij Alekseevič 1937-2008 Čubarikov, Vladimir Nikolaevič Multiple trigonometric sums Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics Trigonometrisches Polynom (DE-588)4806392-7 gnd |
| subject_GND | (DE-588)4806392-7 |
| title | Multiple trigonometric sums |
| title_alt | Kratnye trigonometričeskie summy |
| title_auth | Multiple trigonometric sums |
| title_exact_search | Multiple trigonometric sums |
| title_full | Multiple trigonometric sums by G. I. Arhipov ; A. A. Karacuba and V. N. Čubarikov |
| title_fullStr | Multiple trigonometric sums by G. I. Arhipov ; A. A. Karacuba and V. N. Čubarikov |
| title_full_unstemmed | Multiple trigonometric sums by G. I. Arhipov ; A. A. Karacuba and V. N. Čubarikov |
| title_short | Multiple trigonometric sums |
| title_sort | multiple trigonometric sums |
| topic | Trigonometrisches Polynom (DE-588)4806392-7 gnd |
| topic_facet | Trigonometrisches Polynom |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000148148&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000009943 |
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