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標題: Titlebook: Basic Analytic Number Theory; Anatolij A. Karatsuba,Melvyn B. Nathanson Book 1993 Springer-Verlag Berlin Heidelberg 1993 Analytic Number T [打印本頁]

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書目名稱Basic Analytic Number Theory影響因子(影響力)




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作者: 繁榮地區(qū)    時間: 2025-3-21 22:28

作者: bibliophile    時間: 2025-3-22 03:35
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
作者: FAST    時間: 2025-3-22 09:47
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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Integer Points,In 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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Entire Functions of Finite Order,This chapter provides background information from the theory of entire functions that will be used later in the book.
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The Euler Gamma Function,The Euler gamma function . is defined by the equation.where . is Euler’s constant.
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The Riemann Zeta Function,For Re . 1, the.is defined by.It follows from the definition that ζ(s) is an analytic function in the half-plane Re . > 1.
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Prime Numbers in Arithmetic Progressions,necting 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 shall always assume below that . ≤ ..
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,Waring’s Problem,f the solvability in natural numbers .., ..,…,.. of the equation.where . ≥3 and .(.) (Waring’s problem). Waring’s problem generalizes Lagrange’s theorem that every natural number is the sum of four squares.
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Dirichlet L-Functions,e 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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,Waring’s Problem,f the solvability in natural numbers .., ..,…,.. of the equation.where . ≥3 and .(.) (Waring’s problem). Waring’s problem generalizes Lagrange’s theorem that every natural number is the sum of four squares.
作者: 或者發(fā)神韻    時間: 2025-3-27 19:01
Book 1993English 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 tran
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. 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 En
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