Trigonometric Sums in Number Theory and Analysis / / Gennady I. Arkhipov, Anatoly A. Karatsuba, Vladimir N. Chubarikov.

• Superior document: Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package
• VerfasserIn: Arkhipov, Gennady I.,; Chubarikov, Vladimir N.,; Karatsuba, Anatoly A.,
• MitwirkendeR: Shishkova, Maria,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2008]; ©2004
• Year of Publication: 2008
• Language: English
• Series: De Gruyter Expositions in Mathematics , 39
• Physical Description: 1 online resource (554 p.)
• Other title: Frontmatter --; Contents --; Chapter 1. Trigonometric integrals --; Chapter 2. Rational trigonometric sums --; Chapter 3. Weyl sums --; Chapter 4. Mean value theorems for multiple --; trigonometric sums --; Chapter 5. Estimates for multiple trigonometric --; sums --; Chapter 6. Several applications --; Chapter 7. Special cases of the theory of multiple --; 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 --; Backmatter
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110197983; 9783110494969; 9783110637205; 9783110212129; 9783110212136; 9783110209082
• ISSN: 0938-6572
• DOI: 10.1515/9783110197983
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Gennady I. Arkhipov, Anatoly A. Karatsuba, Vladimir N. Chubarikov.

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. 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.