03351nam 2200697 a 450 991081901420332120200520144314.01-283-42839-397866134283943-11-916551-43-11-019798-710.1515/9783110197983(CKB)1000000000520489(EBL)314062(OCoLC)232160057(SSID)ssj0000262322(PQKBManifestationID)11221807(PQKBTitleCode)TC0000262322(PQKBWorkID)10270340(PQKB)10948523(MiAaPQ)EBC314062(DE-B1597)32311(OCoLC)979969285(DE-B1597)9783110197983(Au-PeEL)EBL314062(CaPaEBR)ebr10194907(CaONFJC)MIL342839(PPN)17559662X(PPN)139863931(EXLCZ)99100000000052048920040910d2004 uy 0engurun#---|u||utxtccrTrigonometric sums in number theory and analysis /by G.I. Arkhipov, V.N. Chubarikov, A.A. Karatsuba1st ed.Berlin ;New York Walter de Gruyterc20041 online resource (564 p.)De Gruyter expositions in mathematics ;39Description based upon print version of record.3-11-016266-0 Includes bibliographical references (p. [539]-551) and index.Front matter --Contents --Introduction --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 trigonometric sums --Chapter 8. The Hilbert-Kamke problem and its generalizations --Chapter 9. The padic 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 --BackmatterThe 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.Gruyter expositions in mathematics ;39.Trigonometric sumsTrigonometric sums.512.7SK 180rvkArkhipov Gennadii Ivanovich1632621Chubarikov Vladimir Nikolaevich1763468Karatsuba Anatolii Alekseevich1632623MiAaPQMiAaPQMiAaPQBOOK9910819014203321Trigonometric sums in number theory and analysis4203910UNINA