UID:
almahu_9949462252002882
Format:
1 online resource (554 p.)
ISBN:
9783110197983
,
9783110494969
Series Statement:
De Gruyter Expositions in Mathematics , 39
Content:
Das Buch stellt die von den Autoren entwickelte Theorie der mehrfachen trigonometrischen Summen vor. Einem integrierten Ansatz folgend, erhalten die Autoren Abschätzungen für diese Summen, vergleichbar den klassischen Abschätzungen von I. M. Vinogradov, und verwenden diese, um verschiedene Probleme der analytischen Zahlentheorie zu lösen. Sie untersuchen trigonometrische Integrale, die häufig in der Physik, der mathematischen Statistik und der Analysis anzutreffen sind, und präsentieren rein arithmetische Ergebnisse, die die Lösbarkeit von Gleichungen in ganzen Zahlen betreffen.
Content:
The book presents the theory of multiple trigonometric sums constructed by the authors. Following a unified approach, the authors obtain estimates for these sums similar to the classical I. M. Vinogradov´s estimates and use them to solve several problems in analytic number theory. They investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis, and in addition they present purely arithmetic results concerning the solvability of equations in integers.
Note:
Frontmatter --
,
Contents --
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Chapter 1. Trigonometric integrals --
,
Chapter 2. Rational trigonometric sums --
,
Chapter 3. Weyl sums --
,
Chapter 4. Mean value theorems for multiple --
,
trigonometric sums --
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Chapter 5. Estimates for multiple trigonometric --
,
sums --
,
Chapter 6. Several applications --
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Chapter 7. Special cases of the theory of multiple --
,
trigonometric sums --
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Chapter 8. The Hilbert-Kamke problem and its --
,
generalizations --
,
Chapter 9. The p-adic method in three problems of --
,
number theory --
,
Chapter 10. Estimates of multiple trigonometric --
,
sums with prime numbers --
,
Chapter 11. Some applications of trigonometric sums --
,
and integrals --
,
Chapter 12. Short Kloosterman sums --
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Backmatter
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Issued also in print.
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DG Expositions in Mathematics Backlist eBook Package, De Gruyter, 9783110494969
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2008, De Gruyter, 9783110212129
In:
E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008, De Gruyter, 9783110212136
In:
E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008, De Gruyter, 9783110209082
Additional Edition:
ISBN 9783110162660
Language:
English
Subjects:
Mathematics
DOI:
10.1515/9783110197983
URL:
https://doi.org/10.1515/9783110197983
URL:
https://www.degruyter.com/isbn/9783110197983
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