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Titlebook: Basic Analytic Number Theory; Anatolij A. Karatsuba,Melvyn B. Nathanson Book 1993 Springer-Verlag Berlin Heidelberg 1993 Analytic Number T

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期刊全稱Basic Analytic Number Theory
影響因子2023Anatolij A. Karatsuba,Melvyn B. Nathanson
視頻videohttp://file.papertrans.cn/181/180955/180955.mp4
圖書封面Titlebook: Basic Analytic Number Theory;  Anatolij A. Karatsuba,Melvyn B. Nathanson Book 1993 Springer-Verlag Berlin Heidelberg 1993 Analytic Number T
影響因子This English translation of Karatsuba‘s Basic Analytic Number Theory follows closely the second Russian edition, published in Moscow in 1983. For the English edition, the author has considerably rewritten Chapter I, and has corrected various typographical and other minor errors throughout the the text. August, 1991 Melvyn B. Nathanson Introduction to the English Edition It gives me great pleasure that Springer-Verlag is publishing an English trans- lation of my book. In the Soviet Union, the primary purpose of this monograph was to introduce mathematicians to the basic results and methods of analytic number theory, but the book has also been increasingly used as a textbook by graduate students in many different fields of mathematics. I hope that the English edition will be used in the same ways. I express my deep gratitude to Professor Melvyn B. Nathanson for his excellent translation and for much assistance in correcting errors in the original text. A.A. Karatsuba Introduction to the Second Russian Edition Number theory is the study of the properties of the integers. Analytic number theory is that part of number theory in which, besides purely number theoretic arguments, the metho
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Information Systems and Data Compression . .>0 and.An application of the Theorem on the density distribution of the zeros of the zeta function in the critical strip enables us to obtain a much stronger result (cf. the corollary of Theorem 2).
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Dimensionality Reduction and Quantizatione numbers in an arithmetic progression with difference .≥ 1 and initial term ., where 1≤ .≤ . and(.)=1. This problem is important not only because it generalizes a classical result, but also because it has exceptional importance for the solution of many additive problems in prime number theory (for
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Dimensionality Reduction and Quantizationnecting the sum of values of the function Λ. over the integers lying in a given arithmetic progression with the zeros of an L-function. This explicit formula together with a theorem on the boundary of the zeros of the .-function will yield the prime number theorem for arithmetic progressions. We sha
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Dimensionality Reduction and QuantizationIn this chapter we consider two fundamental problems in the theory of integer points: Gauss’s problem on the number of integer points inside a circle, and the Dirichlet divisor problem. We shall assume that a Cartesian coordinate (.) system has been defined on the plane.
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Lossless Compression of InformationThis chapter provides background information from the theory of entire functions that will be used later in the book.
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