Theory of Functions
Author: Titchmarch E. C.
Publisher:
Published: 1992
Total Pages:
ISBN-13:
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The Riemann Zeta-Function
Author: Anatoly A. Karatsuba
Publisher: Walter de Gruyter
Published: 2011-05-03
Total Pages: 409
ISBN-13: 3110886146
DOWNLOAD EBOOKThe 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
Riemann's Zeta Function
Author: Harold M. Edwards
Publisher: Courier Corporation
Published: 2001-01-01
Total Pages: 338
ISBN-13: 9780486417400
DOWNLOAD EBOOKSuperb 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.
Exploring the Riemann Zeta Function
Author: Hugh Montgomery
Publisher: Springer
Published: 2017-09-11
Total Pages: 300
ISBN-13: 3319599690
DOWNLOAD EBOOKExploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography.
Prime Numbers and the Riemann Hypothesis
Author: Barry Mazur
Publisher: Cambridge University Press
Published: 2016-04-11
Total Pages: 155
ISBN-13: 1107101921
DOWNLOAD EBOOKThis book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Lectures on the Riemann Zeta Function
Author: H. Iwaniec
Publisher: American Mathematical Society
Published: 2014-10-07
Total Pages: 130
ISBN-13: 1470418517
DOWNLOAD EBOOKThe Riemann zeta function was introduced by L. Euler (1737) in connection with questions about the distribution of prime numbers. Later, B. Riemann (1859) derived deeper results about the prime numbers by considering the zeta function in the complex variable. The famous Riemann Hypothesis, asserting that all of the non-trivial zeros of zeta are on a critical line in the complex plane, is one of the most important unsolved problems in modern mathematics. The present book consists of two parts. The first part covers classical material about the zeros of the Riemann zeta function with applications to the distribution of prime numbers, including those made by Riemann himself, F. Carlson, and Hardy-Littlewood. The second part gives a complete presentation of Levinson's method for zeros on the critical line, which allows one to prove, in particular, that more than one-third of non-trivial zeros of zeta are on the critical line. This approach and some results concerning integrals of Dirichlet polynomials are new. There are also technical lemmas which can be useful in a broader context.
The Bloch–Kato Conjecture for the Riemann Zeta Function
Author: John Coates
Publisher: Cambridge University Press
Published: 2015-03-19
Total Pages: 317
ISBN-13: 1316241300
DOWNLOAD EBOOKThere are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that these values are related to the higher K-theory of the ring of integers. Shortly afterwards, Bloch and Kato proposed a Tamagawa number-type conjecture for these values, and showed that it would follow from a result in motivic cohomology which was unknown at the time. This vital result from motivic cohomology was subsequently proven by Huber, Kings, and Wildeshaus. Bringing together key results from K-theory, motivic cohomology, and Iwasawa theory, this book is the first to give a complete proof, accessible to graduate students, of the Bloch–Kato conjecture for odd positive integers. It includes a new account of the results from motivic cohomology by Huber and Kings.
The Riemann Zeta-Function
Author: Aleksandar Ivic
Publisher: Courier Corporation
Published: 2012-07-12
Total Pages: 548
ISBN-13: 0486140040
DOWNLOAD EBOOKThis text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.
Riemann Zeta
Author: Nicholas B. Beeson
Publisher: iUniverse
Published: 2011-12-06
Total Pages: 200
ISBN-13: 1462060366
DOWNLOAD EBOOKYou dont know what it is to be methe drug that I am, the drug I will be, the pure ecstasy. Here, let me cook up some of me! The world is not as it seems. But forget the world for now The City stands alone as the only haven from government oppression, intentionally left so to serve mankind through its technological advances. The price this paradise pays for its creative freedom is deeper in cost than its denizens could ever fathom. The driver has been assigned a position at Civil Central Command, a relatively simple commission in a city with few regulations. However, this job requires much more work to investigate numerous unexplained deaths. People are dyingeverywhere. With hardly any trail to go on, the driver is chasing a wraith. The Citys light of advancement is darkened by death and destruction as two travelers set upon the City and square off in a showdown. The killer is restless How many more must litter the floor?
The Riemann Hypothesis
Author: Peter B. Borwein
Publisher: Springer Science & Business Media
Published: 2008
Total Pages: 543
ISBN-13: 0387721258
DOWNLOAD EBOOKThe Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.
