# The Riemann Zeta Function

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### The Theory of the Riemann Zeta function

Author | : Late Savilian Professor of Geometry E C Titchmarsh,Edward Charles Titchmarsh,Titchmarsh,D. R. Heath-Brown,Titchmarsh, Edward Charles Titchmarsh |

Publsiher | : Oxford University Press |

Total Pages | : 428 |

Release | : 1986 |

Genre | : Mathematics |

ISBN | : 0198533691 |

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The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved "Riemann hypothesis" at its heart. The second edition has been revised to include descriptions of work done in the last forty years and is updated with many additional references; it will provide stimulating reading for postgraduates and workers in analytic number theory and classical analysis.

### The Riemann Zeta Function

Author | : Anatoly A. Karatsuba,S. M. Voronin |

Publsiher | : Walter de Gruyter |

Total Pages | : 409 |

Release | : 2011-05-03 |

Genre | : Mathematics |

ISBN | : 9783110886146 |

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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

### An Introduction to the Theory of the Riemann Zeta Function

Author | : S. J. Patterson |

Publsiher | : Cambridge University Press |

Total Pages | : 135 |

Release | : 1995-02-02 |

Genre | : Mathematics |

ISBN | : 9781316583357 |

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This is a modern introduction to the analytic techniques used in the investigation of zeta functions, through the example of the Riemann zeta function. Riemann introduced this function in connection with his study of prime numbers and from this has developed the subject of analytic number theory. Since then many other classes of 'zeta function' have been introduced and they are now some of the most intensively studied objects in number theory. Professor Patterson has emphasised central ideas of broad application, avoiding technical results and the customary function-theoretic approach. Thus, graduate students and non-specialists will find this an up-to-date and accessible introduction, especially for the purposes of algebraic number theory. There are many exercises included throughout, designed to encourage active learning.

### The Riemann Hypothesis and the Roots of the Riemann Zeta Function

Author | : Samuel W. Gilbert |

Publsiher | : Riemann hypothesis |

Total Pages | : 160 |

Release | : 2009 |

Genre | : Functions, Zeta |

ISBN | : 143921638X |

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The author demonstrates that the Dirichlet series representation of the Riemann zeta function converges geometrically at the roots in the critical strip. The Dirichlet series parts of the Riemann zeta function diverge everywhere in the critical strip. It has therefore been assumed for at least 150 years that the Dirichlet series representation of the zeta function is useless for characterization of the non-trivial roots. The author shows that this assumption is completely wrong. Reduced, or simplified, asymptotic expansions for the terms of the zeta function series parts are equated algebraically with reduced asymptotic expansions for the terms of the zeta function series parts with reflected argument, constraining the real parts of the roots of both functions to the critical line. Hence, the Riemann hypothesis is correct. Formulae are derived and solved numerically, yielding highly accurate values of the imaginary parts of the roots of the zeta function.

### The Riemann Zeta Function

Author | : Aleksandar Ivic |

Publsiher | : Courier Corporation |

Total Pages | : 548 |

Release | : 2012-07-12 |

Genre | : Mathematics |

ISBN | : 9780486140049 |

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"A thorough and easily accessible account."—MathSciNet, Mathematical Reviews on the Web, American Mathematical Society. This extensive survey presents a comprehensive and coherent account of Riemann zeta-function theory and applications. Starting with elementary theory, it examines exponential integrals and exponential sums, the Voronoi summation formula, the approximate functional equation, the fourth power moment, the zero-free region, mean value estimates over short intervals, higher power moments, and omega results. Additional topics include zeros on the critical line, zero-density estimates, the distribution of primes, the Dirichlet divisor problem and various other divisor problems, and Atkinson's formula for the mean square. End-of-chapter notes supply the history of each chapter's topic and allude to related results not covered by the book. 1985 edition.

### Riemann s Zeta Function

Author | : Harold M. Edwards |

Publsiher | : Courier Corporation |

Total Pages | : 338 |

Release | : 2001-01-01 |

Genre | : Mathematics |

ISBN | : 0486417409 |

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Superb high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled “On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics. English translation of Riemann's original document appears in the Appendix.

### The Zeta function of Riemann

Author | : Edward Charles Titchmarsh |

Publsiher | : Unknown |

Total Pages | : 120 |

Release | : 1972 |

Genre | : Functions, Zeta |

ISBN | : UOM:39015049305165 |

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### Zeta Functions over Zeros of Zeta Functions

Author | : André Voros |

Publsiher | : Springer Science & Business Media |

Total Pages | : 163 |

Release | : 2009-11-21 |

Genre | : Mathematics |

ISBN | : 9783642052033 |

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In this text, the famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions)are analyzed through several zeta functions built over those zeros.