02273nam a22002777a 4500 58597 58597 20211115145717.0 211115b ||||| |||| 00| 0 eng d 9789386279828 :Variety Books Publishers & Distributors ;B-10 Street No 2 West Vinod Nagar Delhi 110092 :IM2892 ;02/11/2021 512.73 QUE Queffélec, Hervé Diophantine approximation and Dirichlet Series / Hervé Queffélec & Martine Queffélec New Delhi, India : Hindustan Book Agency , 2013. xii, 232 pages 24cm. 670 Texts and Reading in Mathematics This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of analytic functions in a half-plane. Finally, chapter seven presents the Bagchi-Voronin universality theorems, for the zeta function, and r-tuples of L functions. The proofs, which mix hilbertian geometry, complex and harmonic analysis, and ergodic theory, are a very good illustration of the material studied earlier. Mathematics Algebra 512 Algebra Diophantine approximation -- Mathematical models. Dirichlet series. Queffélec, Hervé Queffélec Martine MDL 0 0 ddc 0 0 MDL SNUL 2021-11-15 Variety Books Publishers & Distributors 670.00 0 512.73 QUE M264 2021-11-15 00:00:00 2021-11-15 MDL FPDA Grant