Trigonometric Sums in Number Theory and Analysis [E-Book].
Karatsuba, Anatoly A.
Arkhipov, Gennady I. / Chubarikov, Vladimir N. / Shishkova, Maria
Berlin : De Gruyter
1 online resource (X, 554 S.)
englisch
9783110162660
9783110197983
De Gruyter Expositions in Mathematics ; 39
Full Text
Main description: 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.
Biographical note: Dr. Gennady I. Arkhipov and Dr. Anatoly A. Karatsuba are working at the Steklov Mathematical Institute of the Russian Academy of Sciences at Moscow, Russia. Vladimir N. Chubarikov is Professor atthe Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University, Russia.
Main description: 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.
Review text: "The book is written very carefully and contains at the beginning of each chapter an introduction which is very well readable. It will certainly replace the former monographies on this theme."J. Schoissengeier in: Monatshefte für Mathematik 1/2006 "The book will be useful for a wide range of mathematicians."EMS newsletter 9/2005