{"product_id":"basic-analytic-number-theory-hardcover-1","title":"Basic Analytic Number Theory - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eAnatolij A. Karatsuba\u003c\/b\u003e (Author), \u003cb\u003eM. B. Nathanson\u003c\/b\u003e (Translator)\u003c\/p\u003e\u003cp\u003eI. Integer Points.-  1. Statement of the Problem, Auxiliary Remarks, and the Simplest Results.-  2. The Connection Between Problems in the Theory of Integer Points and Trigonometric Sums.-  3. Theorems on Trigonometric Sums.-  4. Integer Points in a Circle and Under a Hyperbola.- Exercises.- II. Entire Functions of Finite Order.-  1. Infinite Products. Weierstrass's Formula.-  2. Entire Functions of Finite Order.- Exercises.- III. The Euler Gamma Function.-  1. Definition and Simplest Properties.-  2. Stirling's Formula.-  3. The Euler Beta Function and Dirichlet's Integral.- Exercises.- IV. The Riemann Zeta Function.-  1. Definition and Simplest Properties.-  2. Simplest Theorems on the Zeros.-  3. Approximation by a Finite Sum.- Exercises.- V. The Connection Between the Sum of the Coefficients of a Dirichlet Series and the Function Defined by this Series.-  1. A General Theorem.-  2. The Prime Number Theorem.-  3. Representation of the Chebyshev Functions as Sums Over the Zeros of the Zeta Function.- Exercises.- VI. The Method of I.M. Vinogradov in the Theory of the Zeta Function.-  1. Theorem on the Mean Value of the Modulus of a Trigonometric Sum.-  2. Estimate of a Zeta Sum.-  3. Estimate for the Zeta Function Close to the Line ? = 1.-  4. A Function-Theoretic Lemma.-  5. A New Boundary for the Zeros of the Zeta Function.-  6. A New Remainder Term in the Prime Number Theorem.- Exercises.- VII. The Density of the Zeros of the Zeta Function and the Problem of the Distribution of Prime Numbers in Short Intervals.-  1. The Simplest Density Theorem.-  2. Prime Numbers in Short Intervals.- Exercises.- VIII. Dirichlet L-Functions.-  1. Characters and their Properties.-  2. Definition of L-Functions and their Simplest Properties.-  3. The Functional Equation.-  4. Non-trivial Zeros; Expansion of the Logarithmic Derivative as a Series in the Zeros.-  5. Simplest Theorems on the Zeros.- Exercises.- IX. Prime Numbers in Arithmetic Progressions.-  1. An Explicit Formula.-  2. Theorems on the Boundary of the Zeros.-  3. The Prime Number Theorem for Arithmetic Progressions.- Exercises.- X. The Goldbach Conjecture.-  1. Auxiliary Statements.-  2. The Circle Method for Goldbach's Problem.-  3. Linear Trigonometric Sums with Prime Numbers.-  4. An Effective Theorem.- Exercises.- XI. Waring's Problem.-  1. The Circle Method for Waring's Problem.-  2. An Estimate for Weyl Sums and the Asymptotic Formula for Waring's Problem.-  3. An Estimate for G(n).- Exercises.- Hints for the Solution of the Exercises.- Table of Prime Numbers\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 240\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.56 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e November 19, 1992\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":46592408518853,"sku":"9783540533450","price":173.8,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0757\/6718\/5605\/files\/IrLPbmvaBF9783540533450_ca2973a8-27dc-4157-be4d-3f8c8035769a.webp?v=1785061306","url":"https:\/\/selloorium.com\/products\/basic-analytic-number-theory-hardcover-1","provider":"Selloorium","version":"1.0","type":"link"}