This text begins with a discussion of general lemmas and advances to an investigation of Waring's problem, including explorations of singular series, the contribution of the basic intervals, and an estimate for G(n). Further topics include approximation by the fractional parts of the values of a polynomial, estimates for Weyl sums, much more. 1954 edition.
Method of Trigonometrical Sums in the Theory of Numbers (Dover Books on Mathematics) (English Edition) Kindle电子书
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美国亚马逊： 2 条评论
Proves big results from scratch, but uses elaborate and hard to parse lemmas2016年4月11日 - 已在美国亚马逊上发表
Vinogradov works out from scratch some powerful results in this book. The reader should first read the chapters in Hardy and Wright on continued fractions and Diophantine approximation, and should also be comfortable with Fourier series; also, things like the elementary symmetric polynomials and Newton's identities are used. Aside from these, only basic manipulations and inequalities are used, but these are supremely complicated. The best reader for the book would be a senior undergraduate student interested in analytic number theory, and the first chapter needs to be read line by line because the results in it are used throughout the book. Books covering similar topics are Nathanson, Additive Number Theory The Classical Bases (Graduate Texts in Mathematics), which is both detailed and well organized, and Vaughan, The Hardy-Littlewood Method (Cambridge Tracts in Mathematics), which is elegant but takes big steps that make it hard to follow for someone learning the subject.
a rare book2005年7月13日 - 已在美国亚马逊上发表
The book get a very clear view about the trigonometrical sums in number theory and it's not so easy to find a work like this in the specialized literature.By the way it is a work of "first hand" that means that the author is one of the most important theorist in this field and much of the topics are originals.Last but not least the price is very very good.